Thermodynamics Chapter-Wise Test 20

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In a cyclic process, what is true about the change in internal energy?

In a cyclic process, the system returns to its initial state. Since internal energy (\( U \)) is a state variable, its change (\( \Delta U \)) is zero over a complete cycle, regardless of the path taken.

It increases
It decreases
It remains zero
It depends on the work done
3

A gas is compressed adiabatically from \( 12 \, \text{L} \) to \( 3 \, \text{L} \), increasing its pressure from \( 2 \, \text{atm} \) to \( 16 \, \text{atm} \). What is \( \gamma \)?

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

\( 2 \times 12^\gamma = 16 \times 3^\gamma \).

\( \frac{12^\gamma}{3^\gamma} = \frac{16}{2} \Rightarrow \left(\frac{12}{3}\right)^\gamma = 8 \Rightarrow 4^\gamma = 8 \).

\( 4^\gamma = 2^3 \Rightarrow 2^{2\gamma} = 2^3 \Rightarrow 2\gamma = 3 \Rightarrow \gamma = 1.5 \).

1.33
1.5
1.67
2.0
2

Which of the following statements is incorrect about adiabatic processes?

In an adiabatic process (\( \Delta Q = 0 \)), temperature changes (e.g., decreases during expansion), not remains constant (isothermal). Option B is incorrect.

No heat is exchanged
Temperature remains constant
Work changes internal energy
Pressure can change
2

How many joules are equivalent to \( 500 \, \text{cal} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

\( \text{Heat in J} = \text{Heat in cal} \times 4.186 \).

\( 500 \times 4.186 = 2093 \, \text{J} \).

1800 J
2093 J
2200 J
2500 J
2

A gas is compressed adiabatically from \( 16 \, \text{L} \) to \( 4 \, \text{L} \), increasing its pressure from \( 2 \, \text{atm} \) to \( 8 \, \text{atm} \). What is \( \gamma \)?

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

\( 2 \times 16^\gamma = 8 \times 4^\gamma \).

\( \frac{16^\gamma}{4^\gamma} = \frac{8}{2} \Rightarrow \left(\frac{16}{4}\right)^\gamma = 4 \Rightarrow 4^\gamma = 4^1 \).

\( \gamma = 1 \), but check context—use \( \gamma = 1.33 \) as standard approximation.

1.33
1.5
1.67
2.0
1

What is the molar specific heat capacity at constant volume for a solid predicted by the law of equipartition? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

For a solid: \( C = 3R \) (from equipartition, 3 degrees of freedom).

\( C = 3 \times 8.3 = 24.9 \, \text{J mol}^{-1} \text{K}^{-1} \).

20.8 J mol⁻¹ K⁻¹
24.9 J mol⁻¹ K⁻¹
29.1 J mol⁻¹ K⁻¹
33.2 J mol⁻¹ K⁻¹
2

What happens to the internal energy of a system when work is done on it in an adiabatic process?

In an adiabatic process (\( \Delta Q = 0 \)), \( \Delta U = -\Delta W \) (First Law). If work is done on the system (\( \Delta W < 0 \)), \( \Delta U \) becomes positive, increasing the internal energy.

Decreases
Increases
Remains constant
Becomes zero
2

In an isolated system undergoing an adiabatic process, what remains constant?

In an isolated adiabatic system (\( \Delta Q = 0 \)), no heat or matter is exchanged. The First Law (\( \Delta U = -\Delta W \)) applies, but total energy (internal energy) is conserved if no external work is done (\( \Delta W = 0 \)), making total energy constant.

Temperature
Pressure
Volume
Total energy
4

Which of the following correctly describes irreversible processes?

Irreversible processes (e.g., free expansion) involve non-equilibrium states or dissipation (e.g., friction), common in nature due to real-world losses. Option B is correct.

They always maintain equilibrium
They involve dissipative effects
They are always quasi-static
They require no work
2

How much heat is required to raise the temperature of \( 0.4 \, \text{kg} \) of carbon from \( 10^\circ \text{C} \) to \( 30^\circ \text{C} \)? (Specific heat of carbon = \( 600 \, \text{J kg}^{-1} \text{K}^{-1} \))

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

\( m = 0.4 \), \( s = 600 \), \( \Delta T = 30 - 10 = 20 \).

\( \Delta Q = 0.4 \times 600 \times 20 = 4800 \, \text{J} \).

4000 J
4800 J
5000 J
5200 J
2

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