Questions & explanations
1. Which of the following statements correctly describes a reversible process?
- It occurs very quickly.
- It can be reversed without leaving any change in the system and surroundings.
- It always involves friction.
- It is always adiabatic.
Answer: It can be reversed without leaving any change in the system and surroundings.
A reversible process is an idealized process that can be reversed by an infinitesimal change in a variable, and after reversal both the system and surroundings return to their original states without any net change. Option A is incorrect because reversible processes are typically slow to maintain equilibrium. Option C is wrong because friction makes a process irreversible. Option D is false because a reversible process is not necessarily adiabatic; it can be isothermal or other types.
2. Which of the following statements is the Kelvin-Planck statement of the second law of thermodynamics?
- Heat cannot flow from a colder body to a hotter body without the aid of an external agency.
- It is impossible to construct a heat engine that converts all the heat supplied into work without any other effect.
- The entropy of an isolated system always increases.
- The total energy of an isolated system remains constant.
Answer: It is impossible to construct a heat engine that converts all the heat supplied into work without any other effect.
The Kelvin-Planck statement asserts that no heat engine can convert the entire heat absorbed from a reservoir into work; some heat must be rejected to a colder reservoir. Option A is the Clausius statement (heat transfer from cold to hot requires external work). Option C is the entropy statement, which is equivalent but not the Kelvin-Planck wording. Option D is the first law of thermodynamics (conservation of energy).
3. For an ideal gas, the molar specific heat at constant pressure (Cp) and at constant volume (Cv) are related by Mayer's relation. Which of the following is correct?
- Cp - Cv = R/2
- Cp - Cv = R
- Cp - Cv = 2R
- Cp - Cv = 0
Answer: Cp - Cv = R
Mayer's relation for an ideal gas states that Cp - Cv = R, where R is the universal gas constant. This relation arises because at constant pressure, additional heat is needed to do work against the external pressure, making Cp greater than Cv by exactly R per mole. The other options are incorrect: R/2 and 2R are not the correct value, and zero would imply Cp = Cv, which is false for an ideal gas.
4. One mole of an ideal gas at 300 K is expanded isothermally from 1 L to 2 L. Given R = 8.3 J mol⁻¹ K⁻¹ and ln 2 = 0.693, the work done by the gas is approximately:
- 2490 J
- 1729 J
- 830 J
- 0 J
Answer: 1729 J
For isothermal reversible expansion, W = nRT ln(V2/V1). n=1, R=8.3, T=300, ln(2)=0.693 → W ≈ 1×8.3×300×0.693 ≈ 1725.6 J (≈1729 J is the closest rounded option). Option A (2490) might come from using log10 instead of ln, option C from nRT only, and D from no work.
5. Which one of the following correctly defines a thermodynamic system?
- The region of space where thermodynamic variables are measured
- The part of the universe under thermodynamic study separated from the surroundings by a real or imaginary boundary
- The set of all objects that exchange energy with the system
- The region surrounding the experimental setup
Answer: The part of the universe under thermodynamic study separated from the surroundings by a real or imaginary boundary
In thermodynamics, the system is the part of the universe chosen for analysis, separated from the surroundings by a boundary. Options A, C, D describe either the surroundings or an incomplete definition.
6. Which of the following is a state function?
- Work
- Heat
- Internal energy
- Both work and heat
Answer: Internal energy
Internal energy depends only on the state of the system (pressure, volume, temperature), not on the path taken to reach that state. Work and heat are path functions; their values depend on the process.
7. According to the zeroth law of thermodynamics, if body A is in thermal equilibrium with body C and body B is in thermal equilibrium with body C, then:
- A and B are necessarily in thermal equilibrium with each other
- A and B are not in thermal equilibrium with each other
- The temperatures of A and B may be different
- The zeroth law does not make any statement about A and B
Answer: A and B are necessarily in thermal equilibrium with each other
The zeroth law states that if two bodies are each in thermal equilibrium with a third body, they are in thermal equilibrium with each other. This is the basis of temperature measurement.
8. In a thermodynamic process, 200 J of heat is supplied to a system and the system does 80 J of work on the surroundings. The change in internal energy of the system is:
- 280 J
- 200 J
- 120 J
- 80 J
Answer: 120 J
According to the first law, ΔU = Q - W (if work done by the system is taken as positive). Here Q = +200 J, W = +80 J, so ΔU = 200 - 80 = 120 J. The internal energy increases by 120 J.
9. The concept of 'degradation of energy' in thermodynamics refers to:
- The total destruction of energy in any process
- The conversion of mechanical energy into heat, making it less available for useful work
- An increase in the availability of energy for work
- A decrease in the entropy of the system
Answer: The conversion of mechanical energy into heat, making it less available for useful work
Degradation of energy means that while energy is conserved, its quality declines as useful work is converted into less usable thermal energy, increasing entropy and unavailability.
10. On a pressure-volume (P-V) diagram, the work done by a gas during an expansion from volume V1 to V2 is represented by:
- The slope of the curve between V1 and V2
- The area under the curve between V1 and V2
- The product of pressure and volume at the initial state
- The change in internal energy of the gas
Answer: The area under the curve between V1 and V2
The work done by a gas is W = ∫ P dV, which equals the area under the P-V curve between the initial and final volumes. Slope, product, or internal energy do not represent work.
11. For an adiabatic process involving an ideal gas, the relation between pressure (P) and volume (V) is:
- PV = constant
- P V^γ = constant
- P^γ V = constant
- P V^{1/γ} = constant
Answer: P V^γ = constant
In an adiabatic process, no heat exchange occurs, and for an ideal gas, PV^γ = constant, where γ = Cp/Cv. The other relations correspond to isothermal (A) or are incorrect.
12. Which of the following correctly describes a reversible cycle?
- A reversible cycle is one that is performed rapidly to minimize heat loss.
- A reversible cycle is an idealization where all processes are quasi-static and there are no dissipative losses.
- In a reversible cycle, the entropy of the universe always increases.
- A reversible cycle can be easily achieved in real engines.
Answer: A reversible cycle is an idealization where all processes are quasi-static and there are no dissipative losses.
A reversible cycle is an ideal cycle carried out infinitely slowly with no friction or other irreversibilities. It sets an upper limit on efficiency.