Thermodynamics Chapter-Wise Test 21

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A gas expands adiabatically from \( 5 \, \text{atm} \) and \( 10 \, \text{L} \) to \( 1 \, \text{atm} \). What is the final volume? (\( \gamma = 1.33 \))

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

\( 5 \times 10^{1.33} = 1 \times V_2^{1.33} \).

\( V_2^{1.33} = 5 \times 10^{1.33} \).

\( V_2 = (5 \times 10^{1.33})^{1/1.33} = 5^{1/1.33} \times 10 \).

\( 5^{0.7519} \approx 3.43 \), \( V_2 \approx 10 \times 3.43 \approx 34.3 \, \text{L} \).

30 L
34.3 L
38 L
40 L
2

In an isobaric process, \( 0.9 \, \text{moles} \) of gas expand from \( 360 \, \text{K} \) to \( 450 \, \text{K} \). What is the heat supplied if \( C_p = 25.5 \, \text{J mol}^{-1} \text{K}^{-1} \)?

\( \Delta Q = \mu C_p \Delta T \).

\( \mu = 0.9 \), \( C_p = 25.5 \), \( \Delta T = 450 - 360 = 90 \).

\( \Delta Q = 0.9 \times 25.5 \times 90 = 2065.5 \, \text{J} \approx 2066 \, \text{J} \).

1900 J
2066 J
2200 J
2300 J
2

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

For monatomic gas: \( C_v = \frac{3}{2} R \), \( C_p = C_v + R \).

\( C_v = \frac{3}{2} \times 8.3 = 12.45 \).

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

16.6 J mol⁻¹ K⁻¹
20.75 J mol⁻¹ K⁻¹
25.0 J mol⁻¹ K⁻¹
29.1 J mol⁻¹ K⁻¹
2

In a reversible process, what condition must be met regarding the system and surroundings?

A process is reversible if it can be reversed, returning both the system and surroundings to their original states without any net change elsewhere. This requires quasi-static conditions and no dissipative effects like friction.

System gains energy
Surroundings lose energy
Both return to original states
Heat is completely converted to work
3

A gas at 6 atm in an 8 L container is cooled from 50°C to 10°C at constant volume. What is the final pressure?

Isochoric: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). \( P_1 = 6 \, \text{atm} \), \( T_1 = 50 + 273 = 323 \, \text{K} \), \( T_2 = 10 + 273 = 283 \, \text{K} \). \( \frac{6}{323} = \frac{P_2}{283} \Rightarrow P_2 = \frac{6 \times 283}{323} \approx 5.26 \, \text{atm} \).

5.0 atm
5.3 atm
5.5 atm
6.0 atm
2

Which of the following statements is correct about irreversible processes?

Irreversible processes often involve non-equilibrium states (e.g., rapid expansion), preventing full reversal without external effects. Option D is correct.

They are always quasi-static
They have no dissipative effects
They require constant temperature
They involve non-equilibrium states
4

How much heat is required to raise the temperature of \( 0.5 \, \text{kg} \) of carbon from \( 25^\circ \text{C} \) to \( 55^\circ \text{C} \)? (Specific heat of carbon = \( 600 \, \text{J kg}^{-1} \text{K}^{-1} \))

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

\( m = 0.5 \), \( s = 600 \), \( \Delta T = 55 - 25 = 30 \).

\( \Delta Q = 0.5 \times 600 \times 30 = 9000 \, \text{J} \).

8500 J
9000 J
9500 J
10000 J
2

0.3 moles of an ideal gas at 400 K expand adiabatically from 6 atm to 2 atm. If \( \gamma = 1.5 \), what is the final temperature?

Adiabatic: \( T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1} \), \( P V = \mu R T \Rightarrow V_1 = \frac{\mu R T_1}{P_1} = \frac{0.3 \times 8.3 \times 400}{6} = 166 \, \text{L} \), \( V_2 = \frac{0.3 \times 8.3 \times T_2}{2} = 1.245 T_2 \). \( 400 \times 166^{0.5} = T_2 \times (1.245 T_2)^{0.5} \). Solve iteratively or approximate: \( T_2 \approx 318 \, \text{K} \) (via \( P V^\gamma \)).

300 K
318 K
330 K
350 K
2

How much heat is required to raise the temperature of \( 0.2 \, \text{kg} \) of aluminium from \( 45^\circ \text{C} \) to \( 75^\circ \text{C} \)? (Specific heat of aluminium = \( 900 \, \text{J kg}^{-1} \text{K}^{-1} \))

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

\( m = 0.2 \), \( s = 900 \), \( \Delta T = 75 - 45 = 30 \).

\( \Delta Q = 0.2 \times 900 \times 30 = 5400 \, \text{J} \).

5000 J
5400 J
5600 J
5800 J
2

Which of the following statements is correct about \( C_p \) and \( C_v \) for an ideal gas?

For an ideal gas, \( C_p > C_v \) because at constant pressure, heat supplies both internal energy increase and work (\( C_p = C_v + R \)), while at constant volume, heat only increases internal energy. Option A is correct.

\( C_p \) is greater than \( C_v \)
\( C_v \) is greater than \( C_p \)
\( C_p \) equals \( C_v \)
\( C_p \) and \( C_v \) are path-dependent
1

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