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Past Questions — 2010
When a compact disc is illuminated by a source of white light, coloured lines are observed. This is due to
A)
dispersion
B)
diffraction
C)
interference
D)
polarization
A Compact Disc (CD) contains a spiral track of tiny pits and lands that act as a reflection grating. When white light hits the surface, the closely spaced tracks act as a diffraction grating. Diffraction occurs when light waves encounter these periodic structures and bend around them, causing the light to spread and overlap. Because white light consists of different wavelengths (colors), each wavelength is diffracted at a slightly different angle (according to the grating equation d sin θ = nλ). This separates the white light into its constituent colors, creating the observed rainbow-like colored lines.
Why other options are incorrect:
- a. Dispersion: While dispersion also separates white light into colors, it occurs due to the variation of the refractive index of a medium with wavelength (e.g., light passing through a glass prism). A CD is a reflective surface, not a refractive medium.
- c. Interference: While diffraction is a form of interference (the superposition of waves from different parts of the wavefront), the specific mechanism of a grating creating a spectrum is categorized as diffraction.
- d. Polarization: Polarization refers to the orientation of the oscillations of the light wave and does not cause the separation of white light into colors.
Which one of the following statements is true?
A)
Both light and sound waves can travel in vacuum
B)
Both light and sound waves in air are transverse
C)
The sound waves in air are longitudinal, while the light waves are transverse
D)
Both light and sound waves in air are longitudinal
To determine the correct statement, we must analyze the fundamental properties of sound and light waves:
1. **Nature of Sound Waves**: Sound is a mechanical wave that requires a medium (solid, liquid, or gas) to propagate. In air, sound travels as a series of compressions and rarefactions where the particles of the medium vibrate parallel to the direction of wave propagation. This is the definition of a **longitudinal wave**. Therefore, sound cannot travel in a vacuum.
2. **Nature of Light Waves**: Light is an electromagnetic wave consisting of oscillating electric and magnetic fields. These fields oscillate perpendicular to the direction of wave propagation, which is the definition of a **transverse wave**. Unlike sound, electromagnetic waves do not require a medium and can travel through a vacuum.
Evaluating the options:
- **Option a**: Incorrect. Sound waves cannot travel in a vacuum.
- **Option b**: Incorrect. Sound waves in air are longitudinal, not transverse.
- **Option c**: Correct. It accurately identifies sound waves in air as longitudinal and light waves as transverse.
- **Option d**: Incorrect. Light waves are transverse, not longitudinal.
Suppose temperature of the sun goes down by a factor of two, then the total power emitted by the sun will go down by a factor of
A)
2
B)
4
C)
8
D)
16
The total power emitted by a blackbody (like the sun) is governed by the Stefan-Boltzmann Law. According to this law, the total power (P) emitted per unit surface area of a blackbody is proportional to the fourth power of its absolute temperature (T). The formula is expressed as: P = σAT⁴, where σ is the Stefan-Boltzmann constant and A is the surface area.
1. Let the initial temperature be T₁ and the initial power be P₁ = σAT₁⁴.
2. The problem states the temperature goes down by a factor of two, so the new temperature T₂ = T₁ / 2.
3. The new power P₂ = σA(T₂⁴) = σA(T₁ / 2)⁴.
4. Simplifying the expression: P₂ = σA(T₁⁴ / 2⁴) = σA(T₁⁴ / 16).
5. Comparing P₂ to P₁: P₂ = P₁ / 16.
Therefore, the total power emitted by the sun will go down by a factor of 16. Options a, b, and c are incorrect because they assume linear, squared, or cubed relationships, whereas the physical law dictates a fourth-power relationship.
A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth, the maximum height attained by the body is
A)
R/6
B)
R/3
C)
2R/3
D)
R
Energy conservation: v=ve/2 ⇒ 1/(R+h)=3/(4R) ⇒ h=R/3.
The unit of Stefan’s constant in S I are
A)
J s-1 m-2 K-4
B)
W s-1 m-2K
C)
J m-2K-4
D)
W m-2 K-4
Stefan-Boltzmann Law states that the total energy radiated per unit surface area of a black body per unit time (emissive power, E) is directly proportional to the fourth power of its absolute temperature (T). The formula is given by: E = σT⁴, where σ is the Stefan-Boltzmann constant.
1. Analyze the units of the variables:
- E (Emissive Power) = Energy per unit area per unit time = (Joules) / (square meters × seconds) = J s⁻¹ m⁻².
- Since 1 Watt (W) = 1 Joule per second (J s⁻¹), the unit of E is W m⁻².
- T (Absolute Temperature) is measured in Kelvin (K).
2. Rearrange the formula to solve for σ:
σ = E / T⁴
3. Substitute the units:
Unit of σ = (W m⁻²) / (K⁴) = W m⁻² K⁻⁴.
Comparing this to the options:
- Option (a) J s-1 m-2 K-4 is equivalent to W m-2 K-4, but standard notation for the constant usually uses Watts or Joules/sec. However, looking at the options provided, (d) is the most standard representation of the unit.
- Option (b) is incorrect as it includes s-1 and K instead of K-4.
- Option (c) is incorrect as it lacks the time component (seconds/Watts).
- Option (d) W m-2 K-4 matches the derived unit perfectly.
The internal energy of a real gas is independent of
A)
temperature
B)
pressure
C)
volume
D)
None of these
To solve this, we must distinguish between an Ideal Gas and a Real Gas.
1. **Ideal Gas:** According to Joule's Law, the internal energy (U) of an ideal gas depends solely on temperature (T). This is because there are no intermolecular forces of attraction or repulsion between the molecules of an ideal gas. Therefore, for an ideal gas, internal energy is independent of pressure and volume.
2. **Real Gas:** In a real gas, intermolecular forces (Van der Waals forces) exist. The internal energy of a real gas consists of two components: kinetic energy (which depends on temperature) and potential energy (which depends on the distance between molecules, and thus depends on volume and pressure).
3. **Analysis of Options:**
- **Temperature (a):** Internal energy always depends on temperature because temperature is a measure of the average kinetic energy of the molecules.
- **Pressure (b) and Volume (c):** Because real gases have intermolecular attractions, changing the volume or pressure changes the average distance between molecules, which alters the potential energy component of the internal energy.
Since the internal energy of a real gas depends on temperature, pressure, and volume, it is NOT independent of any of these variables. Therefore, the correct option is 'None of these'.
Which of the following quantity is always positive in a S.H.M.?
A)
F.a
B)
v.r
C)
a.r
D)
F.r
In Simple Harmonic Motion (S.H.M.), the restoring force (F) is directly proportional to the displacement (r) from the equilibrium position and acts in the opposite direction. This is expressed by the equation: F = -kr, where k is the force constant. According to Newton's Second Law, F = ma, where 'm' is the mass and 'a' is the acceleration. Therefore, F and a are always in the same direction (since mass m is always positive). The dot product of two vectors in the same direction is the product of their magnitudes: F · a = |F||a| cos(0°) = |F||a|. Since magnitudes are always non-negative and the vectors are collinear and codirectional, F · a is always positive (or zero at the equilibrium point).
Evaluating other options:
- b. v · r: Velocity (v) and displacement (r) are in the same direction when moving away from equilibrium and opposite when moving toward it. Thus, v · r can be positive or negative.
- c. a · r: Since a = - (k/m)r, acceleration and displacement are always in opposite directions. Therefore, a · r = |a||r| cos(180°) = -|a||r|, which is always negative.
- d. F · r: Since F = -kr, force and displacement are always in opposite directions. Therefore, F · r = |F||r| cos(180°) = -|F||r|, which is always negative.
When applied to solar radiation, Planck’s law reduces to Wien’s law in the
A)
ultraviolet region
B)
microwave region
C)
infrared region
D)
visible region
Planck's Law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The formula is given by: B(λ, T) = (2hc²/λ⁵) / (exp(hc/λkT) - 1).
Wien's Approximation (Wien's Distribution Law) is a simplification of Planck's Law. It is valid when the term (hc/λkT) is much larger than 1 (hc/λkT >> 1). In this limit, the '-1' in the denominator of Planck's equation becomes negligible, and the expression reduces to: B(λ, T) ≈ (2hc²/λ⁵) exp(-hc/λkT).
For solar radiation (where the surface temperature of the sun is approximately 5778 K), the condition hc/λkT >> 1 is satisfied when the wavelength λ is very small. Small wavelengths correspond to the high-frequency, high-energy end of the spectrum, which is the ultraviolet (UV) region.
Conversely, for very long wavelengths (infrared or microwave regions), the Rayleigh-Jeans law is the appropriate approximation of Planck's law, as the term (hc/λkT) becomes very small.
Golden view of sea shell is due to
A)
diffraction
B)
dispersion
C)
polarization
D)
reflection
The iridescent or 'golden' colors seen on the surface of sea shells (such as nacre or mother-of-pearl) are caused by the phenomenon of diffraction and interference. The inner layer of these shells consists of microscopic, parallel plates of aragonite (calcium carbonate) separated by organic layers. When light hits these periodic structures, it is diffracted and interferes constructively or destructively depending on the wavelength and the angle of observation. This results in the shifting, rainbow-like colors known as iridescence.
Why other options are incorrect:
- b. Dispersion: This is the splitting of white light into its constituent colors through a medium with a varying refractive index (like a prism). While it produces colors, it does not create the structural iridescence seen in shells.
- c. Polarization: This refers to the orientation of light wave oscillations. While it can affect how light is reflected, it is not the cause of the multi-colored appearance of shells.
- d. Reflection: Simple specular reflection only reflects the color of the light source; it does not split light into a spectrum of colors unless combined with interference or diffraction.
The temperature of the sun (5000ºC) is measured with
A)
Platinum resistance thermometer
B)
Gas thermometer
C)
Pyrometer
D)
Vapour pressure thermometer
The measurement of temperature depends on the range of the temperature being measured.
1. **Pyrometer (Correct):** A pyrometer is a non-contact temperature sensor that measures the thermal radiation emitted by an object. It is specifically designed for very high temperatures (typically above 1000°C) where physical contact with the object would destroy the sensor or is physically impossible (such as measuring the temperature of the sun or a blast furnace). Since the sun's temperature is approximately 5000°C, a pyrometer is the only viable instrument among the choices.
2. **Platinum Resistance Thermometer (Incorrect):** These operate on the principle that the electrical resistance of platinum increases with temperature. They are highly accurate but are limited to a range of approximately -200°C to 850°C.
3. **Gas Thermometer (Incorrect):** These use the pressure or volume of a gas as the thermometric property. While they are used as primary standards for calibrating other thermometers, they cannot be used to measure the temperature of the sun due to the requirement of a contained gas volume in contact with the heat source.
4. **Vapour Pressure Thermometer (Incorrect):** These measure temperature based on the pressure of a saturated vapor. They are typically used for lower temperature ranges and cannot withstand or measure the extreme temperatures of stars.
The internal energy of a perfect gas is
A)
partly kinetic and partly potential
B)
wholly potential
C)
wholly kinetic
D)
depends on the ratio of two specific heats
1. Definition of a Perfect Gas: A perfect gas (often used interchangeably with an ideal gas in this context) is a theoretical gas composed of point masses that move randomly and collide elastically.
2. Intermolecular Forces: The fundamental assumption of a perfect/ideal gas is that there are no intermolecular forces of attraction or repulsion between the gas molecules.
3. Potential Energy: In thermodynamics, internal potential energy arises from the forces of attraction or repulsion between molecules. Since these forces are assumed to be zero for a perfect gas, the internal potential energy is zero.
4. Kinetic Energy: The internal energy of a gas consists of the sum of the kinetic energies of its molecules (translational, rotational, and vibrational). For a perfect gas, the internal energy is solely a function of temperature and consists entirely of this kinetic energy.
5. Conclusion: Because there is no potential energy component, the internal energy of a perfect gas is wholly kinetic.
Comparison with other options:
- Option (a) describes a real gas, where intermolecular forces exist.
- Option (b) is incorrect as gases possess kinetic energy due to molecular motion.
- Option (d) is incorrect because while the specific heat ratio (gamma) relates to the degrees of freedom, the nature of the energy itself remains kinetic.
In Rayleigh scattering, the amount of scattered light is proportional to
A)
1/λ
B)
1/λ^2
C)
1/λ^3
D)
1/λ^4
Rayleigh scattering occurs when light is scattered by particles that are much smaller than the wavelength of the light (such as gas molecules in the atmosphere). According to the Rayleigh scattering law, the intensity of the scattered light (I) is inversely proportional to the fourth power of the wavelength (λ). Mathematically, this is expressed as I ∝ 1/λ⁴. This explains why shorter wavelengths (blue light) are scattered much more efficiently than longer wavelengths (red light), which is why the sky appears blue during the day and the sun appears red at sunset. Options a, b, and c are incorrect because they do not follow the derived physical law for scattering by small particles.
Deviation produced in a grating is independent of
A)
wavelength of light
B)
grating constant or element
C)
refractive index of grating material
D)
None of these
The deviation (diffraction angle) produced by a diffraction grating is governed by the grating equation: d sin(θ) = nλ, where 'd' is the grating element (the distance between two adjacent slits), 'θ' is the angle of diffraction (deviation), 'n' is the order of the spectrum, and 'λ' is the wavelength of the incident light.
1. Wavelength (λ): The equation shows that sin(θ) is directly proportional to λ. Therefore, deviation depends on the wavelength of light (Option a is incorrect).
2. Grating constant/element (d): The equation shows that sin(θ) is inversely proportional to d. Therefore, deviation depends on the grating constant (Option b is incorrect).
3. Refractive Index: A diffraction grating works on the principle of interference of light waves originating from multiple slits. Unlike a prism, where deviation is caused by refraction (and thus depends on the refractive index of the material), a grating's deviation is a result of diffraction and interference. The material's refractive index does not enter the grating equation. Thus, the deviation is independent of the refractive index of the grating material (Option c is correct).
A thermo flask is polished well
A)
to make it attractive
B)
for shining
C)
to absorb all radiation from outside
D)
to reflect all radiation from outside
A thermo flask (Dewar flask) is designed to minimize heat transfer between the contents of the flask and the external environment. Heat transfer occurs via three mechanisms: conduction, convection, and radiation.
1. Conduction and Convection are minimized by creating a vacuum between the double walls of the flask.
2. Radiation is the transfer of heat via electromagnetic waves, which does not require a medium. To minimize heat loss or gain via radiation, the inner surfaces of the glass walls are silvered or polished.
According to the laws of thermodynamics and heat transfer, a highly polished, shiny surface has low emissivity and low absorptivity, meaning it reflects most of the incident thermal radiation. Therefore, polishing the flask ensures that radiation from the outside is reflected away (preventing heat gain) and radiation from the inside is reflected back (preventing heat loss).
- Option (a) and (b) are aesthetic reasons and not functional thermodynamic reasons.
- Option (c) is incorrect because absorbing radiation would increase the heat transfer, defeating the purpose of the flask.
In Rayleigh scattering, the degree of scatterimg is proportional to fourth power of wavelength, but the size of the scattering medium’s particles should be such that
A)
size of particles is at least four times the wavelength used
B)
size of particles is 1/4th the wavelength of light
C)
size of particles should be less than the wavelength of light used
D)
size should be equal to wavelength
Rayleigh scattering occurs when light interacts with particles that are significantly smaller than the wavelength of the incident light. Specifically, the condition for Rayleigh scattering is that the particle radius (r) must be much smaller than the wavelength (λ), typically expressed as r << λ. Under this condition, the intensity of the scattered light is inversely proportional to the fourth power of the wavelength (I ∝ 1/λ⁴), which explains why shorter wavelengths (blue light) are scattered more than longer wavelengths (red light), making the sky appear blue. If the particles were equal to or larger than the wavelength, the scattering would follow different laws, such as Mie scattering (where scattering is less dependent on wavelength) or geometric optics (where particles are much larger than the wavelength). Therefore, option (c) is the correct requirement for the Rayleigh regime.
Orbital velocity of a satellite revolving round the earth is independent of the
A)
mass of the earth
B)
mass of the satellite
C)
radius of the earth
D)
radius of the orbit
To find the orbital velocity of a satellite, we equate the gravitational force providing the centripetal force required for circular motion.
1. Gravitational Force: F = (G * M * m) / r²
2. Centripetal Force: F = (m * v²) / r
Where:
- G is the universal gravitational constant
- M is the mass of the Earth
- m is the mass of the satellite
- v is the orbital velocity
- r is the radius of the orbit (distance from the center of the Earth)
Equating the two:
(m * v²) / r = (G * M * m) / r²
Dividing both sides by 'm' and multiplying by 'r':
v² = (G * M) / r
v = sqrt(GM / r)
From this formula, it is evident that the orbital velocity (v) depends on the mass of the central body (M) and the radius of the orbit (r). It does NOT depend on the mass of the satellite (m), as the mass of the satellite cancels out during the derivation. Therefore, whether the satellite is a small cube or a massive space station, if they are in the same orbit, they must travel at the same velocity to maintain that orbit.
If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of roughly
A)
2
B)
4
C)
8
D)
16
The rate of energy emitted by a celestial body like the sun is governed by the Stefan-Boltzmann Law. According to this law, the total power (energy per unit time) radiated from a black body is proportional to the fourth power of its absolute temperature (T). The formula is given by: P = εσAT⁴, where P is the power, ε is the emissivity, σ is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature.
1. Let the initial temperature of the sun be T₁ and the initial rate of energy received on earth be P₁.
2. If the temperature is doubled, the new temperature T₂ = 2T₁.
3. The new rate of energy emitted (and consequently received on earth, assuming distance remains constant) is P₂ ∝ (T₂)⁴.
4. Substituting T₂ = 2T₁, we get P₂ ∝ (2T₁)⁴ = 16(T₁)⁴.
5. Therefore, P₂ / P₁ = 16.
The rate of energy received on earth will increase by a factor of 16. Options a, b, and c are incorrect because they represent linear, squared, and cubed relationships, whereas radiative heat transfer follows a T⁴ relationship.
The running of a fan makes us comfortable during summer, because it
A)
decreases the temperature of air
B)
increases the thermal conductivity of air
C)
increase the rate of evaporation of perspiration
D)
cuts off the thermal radiation reaching us
Step-by-step reasoning: 1. A fan does not cool the air; it simply moves the air around. Therefore, it does not decrease the ambient temperature (eliminating option a). 2. Thermal conductivity is a physical property of the air itself and is not changed by the movement of the fan (eliminating option b). 3. The human body cools itself through the evaporation of sweat (perspiration). Evaporation is a cooling process because it absorbs latent heat from the skin. 4. The rate of evaporation depends on the concentration of water vapor in the air immediately surrounding the skin. A fan blows away the saturated air layer (boundary layer) and replaces it with drier air, which significantly increases the rate of evaporation. 5. This increased evaporation removes heat from the body more quickly, making us feel cooler. 6. A fan does not block thermal radiation from the sun or surroundings (eliminating option d).
If the temperature of the source is increased, the efficiency of the Carnot’s engine
A)
increases
B)
decreases
C)
remains constant
D)
first increases and then remains constant
Carnot efficiency η=1-Tc/Th, increasing Th raises η.
At 0K which of the following properties of a gas will be zero?
A)
Kinetic energy
B)
Potential energy
C)
Mass
D)
Density
1. Definition of Absolute Zero: 0K (Kelvin) is known as absolute zero, the lowest possible temperature theoretically achievable.
2. Kinetic Theory of Gases: According to the kinetic molecular theory, the temperature of a gas is a direct measure of the average kinetic energy of its molecules. The relationship is expressed as KE = (3/2)kT, where k is the Boltzmann constant and T is the absolute temperature.
3. Analysis at 0K: When T = 0K, the mathematical product (3/2)k(0) equals zero. This implies that at absolute zero, the translational motion of the molecules ceases, and the kinetic energy becomes zero (classically).
4. Evaluating other options:
- Potential energy (b) does not become zero; in fact, intermolecular forces (van der Waals forces) still exist, and potential energy depends on the position of molecules relative to each other.
- Mass (c) is an intrinsic property of matter and remains constant regardless of temperature.
- Density (d) is mass per unit volume. While a gas may liquefy or solidify at 0K (increasing density), the density itself does not become zero; it actually increases as the volume decreases.
For a rigid sphere of radius a the scattering cross-section is given by
A)
2 pa2
B)
3 pa2
C)
4 pa2
D)
pa2
In the context of atomic and nuclear physics, the scattering of particles by a rigid sphere (hard sphere scattering) is a fundamental problem. For a hard sphere of radius 'a', the total scattering cross-section (σ) is calculated based on the impact parameter. In the classical limit, any particle with an impact parameter b < 2a will strike the sphere and be scattered. However, the standard result for the total cross-section of a hard sphere in the low-energy (s-wave) limit of quantum mechanics, or the effective area presented by the sphere for scattering, is given by σ = 4πa². This is exactly four times the geometric cross-section (πa²) of the sphere. This phenomenon occurs because the wave nature of the particle leads to diffraction-like scattering, effectively doubling the radius of the interaction in the cross-section calculation (σ = π(2a)² = 4πa²). Note: In the options provided, 'p' is used as a typographical representation of the mathematical constant π (pi).
In an elliptically polarized light, the amplitude of vibrations
A)
changes in magnitude
B)
changes in direction
C)
remains constant
D)
both (a) and (b)
To understand elliptically polarized light, we must look at the behavior of the electric field vector (the vibration) as it propagates.
1. **Definition**: Elliptical polarization occurs when two orthogonal linear polarizations (e.g., along the x and y axes) are combined with a phase difference that is not an integer multiple of π/2 (or if they are π/2 out of phase but have different amplitudes).
2. **Change in Direction**: In any form of polarization other than linear, the direction of the electric field vector rotates as the wave propagates. In elliptical polarization, the vector traces an ellipse in the plane perpendicular to the direction of propagation. Therefore, the direction changes continuously (Option b is correct).
3. **Change in Magnitude**: In linear polarization, the amplitude is constant. In circular polarization, the amplitude is also constant. However, in elliptical polarization, the distance from the origin to the tip of the electric field vector (the magnitude of the vibration) varies as it traces the elliptical path. It reaches a maximum along the major axis and a minimum along the minor axis of the ellipse. Therefore, the magnitude changes (Option a is correct).
Since both the magnitude and the direction of the vibrations change over time/space, the correct answer is both (a) and (b).
Energy is not carried by
A)
transverse progressive wave
B)
longitudinal progressive wave
C)
stationary wave
D)
electromagnetic wave
To determine which wave does not carry energy, we must distinguish between progressive waves and stationary waves:
1. **Progressive Waves (Options a, b, and d):** A progressive wave (whether transverse, longitudinal, or electromagnetic) is a wave that travels through a medium or space, transporting energy from one point to another. For example, sound waves (longitudinal) and light waves (electromagnetic) carry energy from the source to the receiver.
2. **Stationary Waves (Option c):** Also known as standing waves, these are formed by the superposition of two identical progressive waves traveling in opposite directions. In a stationary wave, the energy is 'trapped' between the nodes. While the particles of the medium vibrate, there is no net transfer of energy from one position to another along the wave. The energy oscillates between kinetic and potential forms within the antinodes, but the average energy flux across any plane is zero.
Therefore, energy is not carried (transported) by a stationary wave.
As a consequence of Brewster’s law for polarization, it follows that the angle of polarization depends upon
A)
the wavelength of light employed
B)
plane of polarization’s orientation
C)
the amplitude of light employed
D)
None of these
Brewster's Law states that the tangent of the polarizing angle (Brewster's angle, θp) is equal to the ratio of the refractive indices of the two media involved. Mathematically, it is expressed as: tan(θp) = n2 / n1, where n2 is the refractive index of the denser medium and n1 is the refractive index of the rarer medium (usually air, where n1 ≈ 1).
Analyzing the options:
1. Wavelength of light (a): While the refractive index (n) of a material can vary slightly with wavelength (a phenomenon called dispersion), Brewster's Law itself defines the angle based on the refractive index. In the context of standard physics problems regarding the 'consequence' of the law, the angle is a function of the material properties (refractive index), not the wavelength of the light source itself.
2. Plane of polarization's orientation (b): The plane of polarization is a result of the light hitting the surface at the Brewster angle; the angle does not depend on the orientation of the plane.
3. Amplitude of light (c): The refractive index and the resulting angle of polarization are independent of the intensity or amplitude of the incident light.
Since the angle of polarization depends solely on the refractive indices of the two media, and none of the provided options (wavelength, orientation, or amplitude) are the primary determinants defined by Brewster's Law, the correct option is 'None of these'.
The degree of freedom of a triatomic gas is
A)
1
B)
2
C)
6
D)
8
The degree of freedom (f) of a molecule is the number of independent ways in which it can possess energy. For a triatomic gas, we must consider both translational and rotational degrees of freedom.
1. Translational Degrees of Freedom: Every molecule, regardless of its shape, can move in three independent directions (x, y, and z axes). Thus, translational f = 3.
2. Rotational Degrees of Freedom:
- For a linear triatomic molecule (like CO2), there are 2 rotational degrees of freedom (rotation about the axis of the molecule does not count as it has negligible moment of inertia).
- For a non-linear triatomic molecule (like H2O), there are 3 rotational degrees of freedom (rotation about all three principal axes).
3. Total Degrees of Freedom (at room temperature, ignoring vibrations):
- Linear: 3 (trans) + 2 (rot) = 5
- Non-linear: 3 (trans) + 3 (rot) = 6
Comparing these results to the given options:
- Option (a) 1 and (b) 2 are too low for any gas molecule.
- Option (d) 8 would only be possible if vibrational modes were included (which usually occur at very high temperatures).
- Option (c) 6 corresponds to a non-linear triatomic molecule, which is the standard assumption for a general 'triatomic gas' unless 'linear' is specified. Therefore, 6 is the most appropriate answer among the choices provided.