Thermodynamics Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A gas expands adiabatically from \( 3 \, \text{atm} \) and \( 6 \, \text{L} \) to \( 1 \, \text{atm} \). What is the final volume? (\( \gamma = 1.4 \))

\( P_1 V_1^\gamma = P_2 V_2^\gamma \).

\( 3 \times 6^{1.4} = 1 \times V_2^{1.4} \).

\( V_2^{1.4} = 3 \times 6^{1.4} \).

\( V_2 = (3 \times 6^{1.4})^{1/1.4} = 3^{1/1.4} \times 6 \).

\( 3^{0.714} \approx 2.08 \), \( 6^{1.4} \approx 12.29 \), but directly: \( V_2 = 6 \times 3^{1/1.4} \approx 12.48 \, \text{L} \).

10 L
12.5 L
14 L
16 L
2

What property distinguishes intensive variables from extensive variables?

Intensive variables (e.g., pressure, temperature) do not depend on the system’s size or amount, remaining unchanged when the system is divided. Extensive variables (e.g., volume, internal energy) scale with the system’s size.

Dependence on temperature
Independence from system size
Variation with heat transfer
Dependence on work done
2

How much heat is required to vaporize \( 1.5 \, \text{g} \) of water at \( 100^\circ \text{C} \) and \( 1 \, \text{atm} \)? (Latent heat = \( 2256 \, \text{J/g} \))

\( \Delta Q = m L \).

\( m = 1.5 \), \( L = 2256 \).

\( \Delta Q = 1.5 \times 2256 = 3384 \, \text{J} \).

3000 J
3384 J
3500 J
3600 J
2

Which of the following statements is incorrect about internal energy?

Internal energy (\( U \)) is the sum of molecular kinetic and potential energies, a state variable independent of the path. It does not include the system’s macroscopic kinetic energy (e.g., a moving bullet), making option C incorrect.

It is a state function
It depends only on the system’s state
It includes the kinetic energy of the system as a whole
It can change due to heat or work
3

A gas at 5 atm in a 6 L container is heated from 20°C to 60°C at constant volume. What is the final pressure?

Isochoric: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). \( P_1 = 5 \, \text{atm} \), \( T_1 = 20 + 273 = 293 \, \text{K} \), \( T_2 = 60 + 273 = 333 \, \text{K} \). \( \frac{5}{293} = \frac{P_2}{333} \Rightarrow P_2 = \frac{5 \times 333}{293} \approx 5.68 \, \text{atm} \).

5.5 atm
5.7 atm
6.0 atm
6.2 atm
2

How much heat is required to raise the temperature of \( 0.5 \, \text{kg} \) of aluminium from \( 25^\circ \text{C} \) to \( 55^\circ \text{C} \)? (Specific heat of aluminium = \( 900 \, \text{J kg}^{-1} \text{K}^{-1} \))

\( \Delta Q = m s \Delta T \).

\( m = 0.5 \), \( s = 900 \), \( \Delta T = 55 - 25 = 30 \).

\( \Delta Q = 0.5 \times 900 \times 30 = 13500 \, \text{J} \).

12000 J
13500 J
15000 J
16500 J
2

A system releases \( 810 \, \text{J} \) of heat and has \( 270 \, \text{J} \) of work done on it. What is the change in internal energy?

First Law: \( \Delta Q = \Delta U + \Delta W \).

\( \Delta Q = -810 \) (heat released), \( \Delta W = -270 \) (work on system).

\( -810 = \Delta U - 270 \Rightarrow \Delta U = -810 + 270 = -540 \, \text{J} \).

-600 J
-540 J
-500 J
-450 J
2

Which of the following statements is incorrect about work in thermodynamics?

Work (\( W = P \Delta V \)) is mechanical energy transfer, not requiring temperature differences (unlike heat). Option B is incorrect.

It is path-dependent
It requires a temperature difference
It can be positive or negative
It involves volume change
2

What is the molar specific heat capacity at constant pressure for a monatomic gas if \( C_v = 12.45 \, \text{J mol}^{-1} \text{K}^{-1} \) and \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \)?

\( C_p - C_v = R \).

\( C_p = C_v + R = 12.45 + 8.3 = 20.75 \, \text{J mol}^{-1} \text{K}^{-1} \).

18.0 J mol⁻¹ K⁻¹
20.75 J mol⁻¹ K⁻¹
22.0 J mol⁻¹ K⁻¹
25.0 J mol⁻¹ K⁻¹
2

What happens to the temperature of an ideal gas during an adiabatic expansion?

In an adiabatic expansion (\( \Delta Q = 0 \)), the gas does work on the surroundings (\( W > 0 \)), reducing its internal energy (\( \Delta U = -W \)). For an ideal gas, \( U \) depends only on temperature, so temperature decreases.

Increases
Decreases
Remains constant
Becomes zero
2

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