Heat And Thermodynamics
Each of the following questions comprises two statements. The assertion is expressed by Statement 1 and the reason is expressed by Statement 2.
Each question has four options (1), (2), (3), and (4) as given below, out of which only ONE is correct.
- Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
- Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
- Statement 1 is true and Statement 2 is false.
- Statement 1 is false and Statement 2 is true.
- Both Statement 1 and Statement 2 are false.
Some questions are preceded, by a supporting paragraph in addition to the statements.
Kinetic Theory
Question 1. Statement 1 Woolen clothes keep the body warm in winter.
Statement 2 Air is a bad conductor of heat.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Woolen clothes and air are both bad conductors of heat.
Question 2. Statement 1 The temperature near the seaside is moderate.
Statement 2 Water has a high thermal capacity.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Water has a high specific heat capacity (= 4200 J kg-1 K-1), so it cools slowly and also heats up slowly.
Consequently, the amount of heat exchanged in each case is large. Hence, the coastal area has a moderate temperature: neither too hot nor too cold.
Question 3. Statement 1 At room temperature, water does not sublimate from ice to steam.
Statement 2 The critical point of water is much above the room temperature.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
At the triple point, all three phases (solid, liquid, and vapor) coexist. The liquid-vapor boundary terminates at the critical temperature Tc and the critical pressure pc. In water, the critical temperature is around 647 K (374 °C), much higher than room temperature, and at a pressure of around 218 atm.
Question 4. Statement 1 A blue star is at a higher temperature than a red star.
Statement 2 Wien’s displacement law states that \(T \propto \frac{1}{\lambda_{\mathrm{m}}}\)
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
According to Wien’s displacement law, the wavelength λm corresponding to maximum intensity in the radiation graph shifts towards the lower wavelength side with the increase in temperature. Blue light has a lower wavelength compared to the red one, i.e., λblue < λred, hence the temperature of a blue star is more than that of a red star.
Question 5. Statement 1 In a temperature-pressure (p-T) phase diagram of water, the slope of the melting curve is found to be negative.
Statement 2 Ice contracts on melting into water.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The slope of (p-T) phase diagrams for water is negative because during the melting process (ice → water) ice contracts.
Question 6. Statement 1 A piece of ice, with a stone frozen inside it, floats on water in a beaker. When the ice melts, the level of water in the breaker decreases.
Statement 2 The density of stone is more than that of water.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Ice frozen with a stone inside floats on water because the buoyant force is sufficient to balance the weight of (ice + stone). When ice melts, the stone sinks due to its higher density.
Question 7. Statement 1 For a higher temperature, the peak emission wavelength of a black body shifts to the lower-wavelength side.
Statement 2 Peak emission wavelengths of a black body are proportional to the fourth power of temperature.
Answer: 3. Statement 1 is true and Statement 2 is false.
According to Wien’s law, the wavelength, corresponding to the peak emission (λm) shifts towards the lower-wavelength side with an increase in temperature\(\left(\lambda_{\mathrm{m}} \propto \frac{1}{T}\right)\). According to the Stefan-Boltzmann law, the total radiant heat energy emitted is proportional to the fourth power of its absolute temperature.
Question 8. Statement 1 A hollow metallic closed container with a small opening maintained at a high temperature can act as a source of black-body radiation.
Statement 2 All metals act as black-body radiators.
Answer: 3. Statement 1 is true and Statement 2 is false.
Metals have different emissive and absorptive powers, hence they do not act as black bodies. A closed metallic conductor with a cavity and hole (Ferry’s black body) is a near approximation of a black body.
9. Statement 1 Water kept in an open vessel will quickly evaporate on the tire surface of the moon.
Statement 2 The temperature at the surface of the moon is much higher than the boiling point of water.
Answer: 3. Statement 1 is true and Statement 2 is false.
The moon has no atmosphere due to its low escape velocity, so quick evaporation of water is also due to the same reason and not due to the high temperature at the moon’s surface alone.
Question 10. Statement 1 When hot water is poured into a beaker of thick glass, the beaker cracks.
Statement 2 The outer surface of the beaker expands suddenly.
Answer: 3. Statement 1 is true and Statement 2 is false.
Glass has a low thermal conductivity. So, its inner surface absorbs heat and expands, whereas the outer surface does not. This leads to cracking.
Question 11. Statement 1 The radiation from the sun’s surface varies as the fourth power of its absolute temperature.
Statement 2 The sun is not a black body.
Answer: 3. Statement 1 is true and Statement 2 is false.
The sun with an effective temperature of approximately 5800 K is an approximate black body and hence follows Stefan’s law (H ∝ T4) and Wien’s law (λmT = constant)
Question 12. Statement 1 The maximum airflow due to convection does not occur at the north pole but occurs at 30° N.
Statement 2 There is a maximum temperature difference between the equator and 30° N.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The earth’s atmosphere is fixed to the earth by gravity and rotates with it. The heating of the earth’s surface by the sun creates circulation. Due to the earth’s rotation, there is a buildup of air at about 30° N leading to the maximum convection.
Question 13. Statement 1 Perspiration from the human body helps in cooling the body.
Statement 2 A thin layer of water on the skin enhances heat emissivity.
Answer: 3. Statement 1 is true and Statement 2 is false.
Perspiration gives the sensation of cooling because the latent heat required for the evaporation of sweat is derived from the body.
Question 14. Statement 1 The air at some distance above a fire is hotter than the same distance below it.
Statement 2 The air surrounding the fire carries heat upwards.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The air surrounding the fire becomes hot, expands, and becomes lighter. A convection current is built up and cold air comes down.
Question 15. Statement 1 For an ideal gas, at a constant temperature, the product of pressure and volume is constant.
Statement 2 The mean-square velocity of the molecules of a gas is inversely proportional to its mass.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
According to Boyle’s law, pV = constant at a constant temperature. Hence, Statement 1 is true. According to the kinetic theory, the pressure (p) exerted by a gas is
∴ \(p=\frac{1}{3} \frac{M}{V} c_{\mathrm{rms}}^2\)
⇒ mean-square velocity \(\propto \frac{1}{M}\).
Question16. Statement 1 The root-mean-square velocity and the most probable velocity of the molecules in a gas are the same.
Statement 2 The Maxwell distribution for the speed of molecules in a gas is asymmetric.
Answer: 4. Statement 1 is false and Statement 2 is true.
For a gas, RMS velocity = \(\sqrt{\frac{3 R T}{M}}\)
and most-probable velocity = \(\sqrt{\frac{2 R T}{M}}\)
So, Statement 1 is false.
The graph showing the velocity distribution among the molecules is asymmetric, so the reason is true.
Question 17. Statement 1 The size of a hydrogen balloon increases as it rises in air.
Statement 2 The material of the balloon can be easily stretched.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
The balloon expands due to a decrease in atmospheric pressure with height.
Question 18. Statement 1 The ratio cp/cv for a diatomic gas is more than that for a monatomic gas.
Statement 2 The molecules of a monatomic gas have fewer degrees of freedom than those of a diatomic gas.
Answer: 4. Statement 1 is false and Statement 2 is true.
The ratio cp/cv (=γ) is given by \(\gamma=1+\frac{2}{f}\) where f is the degree of freedom.
For monatomic gases, \(\gamma_{\text {mono }}=1+\frac{2}{3}=\frac{5}{3}\) and for diatomic gases, \(\gamma_{\mathrm{di}}=1+\frac{2}{5}=\frac{7}{5}\)
∴γmono > γdi
Question 19. Statement 1 The vibrational energy of a diatomic molecule corresponding to each degree of freedom is kBT.
Statement 2 For every molecule, the vibrational degree of freedom is 2.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Vibrational motion in a diatomic molecule has two types of energy: kinetic and potential, which contributes to 2 degrees of freedom. According to the equipartition law, the energy of vibrational motion is
∴ \(E_{\mathrm{vib}}=2 \cdot \frac{1}{2} k_B T=k_B T\)
Thermodynamics
Question 1. Statement 1 Thermodynamic processes in nature are irreversible.
Statement 2 Dissipative effects cannot be eliminated.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Most of the thermodynamic processes in nature are irreversible due to the presence of dissipative forces like friction, viscosity, etc.
Question 2. Statement 1 In an isolated system, the entropy increases.
Statement 2 The processes in an isolated system are adiabatic.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
According to the second law of thermodynamics, the entropy of an isolated system never decreases because thermodynamic systems always lead toward the thermodynamic equilibrium, a state with the maximum entropy.
In an adiabatic process, no energy or mass transfer takes place between the system and the surroundings.
Question 3. Statement 1 It is not possible for a system unaided by an external agency to transfer heat from one body at a lower temperature to another at a higher temperature.
Statement 2 It is not possible to violate the second law of thermodynamics.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The statement given in Statement 1 is itself the second law of thermodynamics, which cannot be violated.
Question 4. Statement 1 For an isothermal process in an ideal gas, the heat absorbed by the gas is entirely used in the work done by the gas.
Statement 2 During a process taking place in a system, if the temperature remains constant then the process is isothermal.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
According to the first law of thermodynamics,
dQ = dU + dW = ncv dT + dW.
In an isothermal process, the temperature T is constant, so dT = 0; and the total heat given (dQ) is spent in the work done (dW).
Question 5. Statement 1 cp is always greater than cv in gases.
Statement 2 The work done at a constant pressure is more than that at a constant volume.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
cp > cv because more heat is required to increase the temperature by dT, keeping the pressure constant rather than keeping the volume constant. In the former case, a part of the heat energy is spent in doing the work; but in the latter, the entire heat is spent in increasing the temperature, and no work is done.
Question 6. Statement 1 Reversible systems are difficult to find in the real world.
Statement 2 Most processes are dissipative in nature.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Reversible systems are associated with nondissipative processes, which are ideal and impracticable. Dissipative processes correspond to the irreversible nature of forces.
Question 7. Statement 1 The melting point of ice decreases with an increase in pressure.
Statement 2 Ice contracts on melting.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
An increase in pressure decreases the melting point of a solid, which contracts on melting (like ice).
Question 8. Statement 1 Air quickly leaking out of a balloon becomes cooler.
Statement 2 The leaking air undergoes adiabatic expansion.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The rapid leaking of air is an adiabatic expansion, which is associated with cooling.
Question 9. Statement 1 When a glass of hot milk is placed in a room and allowed to cool, its entropy increases.
Statement 2 Allowing hot objects to cool down does not violate the second law of thermodynamics.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
According to the second law of thermodynamics, the total entropy of an isolated system never decreases: it always increases for irreversible processes like the cooling of milk in a room.
Question 10. Statement 1 When a bottle of cold carbonated drink is opened a slight fog forms around the opening.
Statement 2 An adiabatic expansion of the gas causes a lowering of temperature and condensation of water vapor.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
A sudden and fast expansion (an adiabatic process) of dissolved gases in a cold drink is associated with cooling, which causes condensation of water vapor and the formation of fog around the opening.
Question 11. Statement 1 The Carnot cycle is useful in understanding the performance of heat engines.
Statement 2 The Carnot cycle provides a way of determining the maximum possible efficiency achievable with reservoirs of a given temperature.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The Carnot cycle is a theoretical thermodynamic cyclic process that gives the maximum possible efficiency during the conversion of heat into work.
Question 12. Statement 1 The specific heat of a gas in an adiabatic process is zero and in an isothermal process is infinite.
Statement 2 The specific heat of gas is directly proportional to the change of heat in a system and inversely proportional to the change in temperature.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
When the heat ΔQ is either absorbed or expelled, ΔQ = nCΔT, where C is the molar heat capacity, which is process-dependent. For an adiabatic process, ΔQ = 0, so C = 0. For an isothermal process, ΔT = 0, so \(C=\frac{\Delta Q}{n \Delta T}=\infty\).
In both cases, C ∝ ΔQ and \(C \propto \frac{1}{\Delta T}\).
Question 13. Statement 1 During the rapid pumping of air in tires, the air inside the tire becomes hotter than the atmospheric air.
Statement 2 An adiabatic process occurs at a highly rapid rate.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Rapid pumping of air into a tire is an adiabatic compression, which is associated with a rise in temperature.
Question 14. Statement 1 In an adiabatic process, the change in internal energy of a gas is equal to the work done on or by the gas in the process.
Statement 2 The temperature of a gas remains constant in an adiabatic process.
Answer: 3. Statement 1 is true and Statement 2 is false.
In an adiabatic process, the heat exchanged is ΔQ = 0, so ΔU + ΔW = 0, ΔU = -ΔW. This corresponds to the statements of assertion. In an adiabatic process, there is either cooling (during expansion) or heating (during compression).
Question 15. Statement 1 In a pressure cooker, some water is brought to a boil. The cooker is then removed from the stove. Now, after removing the lid of the pressure cooker, the water starts to boil again.
Statement 2 The impurities in water bring down its boiling point.
Answer: 3. Statement 1 is true and Statement 2 is false.
In a pressure cooker, the steam inside builds up a high pressure. This high-pressure steam raises the boiling point of water above the normal 100 °C. When the cooker is removed from the stove and the lid is opened, the pressure again decreases, due to which the boiling point decreases and water starts to boil again.
Question 16. Statement 1 In a gas, any rapid change must be adiabatic whereas a slow change may be adiabatic.
Statement 2 In a p-V diagram, the magnitude of the slope is greater for an adiabatic process than for an isothermal process.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
The process is adiabatic only when there is no exchange of heat between the system and the surroundings (ΔQ = 0). The change may be rapid or slow:
∴ \(\left|\frac{d p}{d V}\right|_{\text {adiabatic }}=\gamma p\).
and \(\left|\frac{d p}{d V}\right|_{\text {isothermal }}=p \text {, with } \gamma=\frac{C_p}{C_V}>1\).
