Question 1

A heat engine receives 1000 J of heat from a hot reservoir and releases 600 J to a cold reservoir in one cycle. What is the efficiency of the engine?

Accepted Answer

The efficiency of a heat engine is η = (Q_in - Q_out) / Q_in = (1000 - 600) / 1000 = 400/1000 = 0.40 = 40%.

Question 2

A gas absorbs 500 J of heat and expands against an external pressure, doing 200 J of work. What is the change in internal energy of the gas?

Accepted Answer

By the first law of thermodynamics, ΔU = Q - W, where Q = 500 J (heat absorbed) and W = 200 J (work done by gas), so ΔU = 500 - 200 = 300 J.

Question 3

Which of the following is an intensive property of a thermodynamic system?

Accepted Answer

Temperature is an intensive property as it does not depend on the amount of substance, unlike volume, mass, and number of moles which are extensive properties.

Question 4

In an adiabatic process, 400 J of work is done on a gas. What is the change in internal energy of the gas?

Accepted Answer

In an adiabatic process, Q = 0 (no heat exchange), so from ΔU = Q - W, we get ΔU = 0 - (-400) = 400 J (work done on gas is negative for the system).

Question 5

A rigid container filled with an ideal gas is heated. Which thermodynamic process does this represent?

Accepted Answer

In a rigid container, the volume remains constant (V = constant), which defines an isochoric process, regardless of heat being added or temperature changing.

Question 6

A system absorbs 500 J of heat and does 200 J of work on the surroundings. What is the change in internal energy of the system?

Accepted Answer

By first law of thermodynamics: ΔU = Q - W = 500 - 200 = 300 J.

Question 7

An ideal gas undergoes an isothermal process at 300 K. If the initial volume is 2 L and final volume is 8 L, what is the work done by the gas? (R = 8.314 J/(mol·K), n = 1 mol)

Accepted Answer

For isothermal process: W = nRT ln(V₂/V₁) = 1 × 8.314 × 300 × ln(4) ≈ 2496 J.

Question 8

Which of the following statements correctly describes the second law of thermodynamics?

Accepted Answer

The second law states that entropy of an isolated system increases for irreversible processes and remains constant for reversible processes.

Question 9

A rigid container holds 2 moles of an ideal gas at 400 K with internal energy 5000 J. The gas is heated until its temperature becomes 500 K. What is the work done by the gas?

Accepted Answer

In a rigid container, volume is constant, so no work is done by or on the gas (W = 0).

Question 10

For an adiabatic process of an ideal gas, which relation correctly represents the process?

Accepted Answer

In an adiabatic process (Q = 0), the relation PVγ = constant holds, where γ is the heat capacity ratio.

Question 11

An ideal gas expands from 1 m³ to 3 m³ at constant pressure of 100 kPa. Calculate the work done by the gas.

Accepted Answer

For isobaric process: W = P(V₂ - V₁) = 100 × (3 - 1) = 200 kJ.

Question 12

The molar heat capacity of a gas at constant volume (Cv) for a diatomic ideal gas is:

Accepted Answer

For a diatomic gas, Cv = (5/2)R due to 3 translational and 2 rotational degrees of freedom.

Question 13

A heat engine receives 1000 J of heat from a hot reservoir and rejects 400 J to a cold reservoir in one cycle. What is the efficiency of the engine?

Accepted Answer

Efficiency η = (Qh - Qc)/Qh = (1000 - 400)/1000 = 0.6 or 60%.

Question 14

A system has internal energy of 8000 J. It absorbs 3000 J of heat and 2000 J of work is done on it. What is the final internal energy?

Accepted Answer

ΔU = Q + W (work done on system) = 3000 + 2000 = 5000 J; Final U = 8000 + 5000 = 13000 J.

Question 15

A gas undergoes an isothermal expansion from volume V₁ = 2 L to V₂ = 8 L at temperature T = 300 K. If the initial pressure is P₁ = 4 atm, calculate the work done by the gas (use ln(4) ≈ 1.39).

Accepted Answer

For isothermal process: W = nRT ln(V₂/V₁) = P₁V₁ ln(V₂/V₁) = 4 × 2 × 1.39 = 11.12 L·atm ≈ 1410 J.

Question 16

One mole of an ideal diatomic gas is heated at constant volume from 300 K to 600 K. Calculate the change in internal energy (R = 8.314 J/(mol·K), Cv = 5R/2 for diatomic gas).

Accepted Answer

ΔU = nCvΔT = 1 × (5/2 × 8.314) × (600 - 300) = 20.785 × 300 ≈ 20,785 J.

Question 17

A heat engine operates between two thermal reservoirs at temperatures TH = 500 K and TC = 300 K. If the engine absorbs 5000 J of heat from the hot reservoir, what is the maximum possible work output?

Accepted Answer

Maximum efficiency is Carnot efficiency: η = 1 - TC/TH = 1 - 300/500 = 0.4; therefore W = η × QH = 0.4 × 5000 = 2000 J.

Question 18

A cylinder containing 2 moles of ideal gas undergoes adiabatic compression. The initial temperature is T₁ = 300 K and final temperature is T₂ = 450 K. Calculate the work done on the gas (Cv = (5/2)R, R = 8.314 J/(mol·K)).

Accepted Answer

In adiabatic process, W = -ΔU = -nCvΔT = -2 × (5/2 × 8.314) × (450 - 300) = -12,471 J; work done on gas = 12,471 J.

Agniveer Army Technical Thermodynamics

Thermodynamics — Practice Questions