NEET Thermodynamics — Set 20

Question 1

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

Accepted Answer

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.

Question 2

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} $)

Accepted Answer

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} $.

Question 3

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 $?

Accepted Answer

$ 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.

NEET Physics: Thermodynamics — Practice Set 20

Q1. In an isolated system undergoing an adiabatic process, what remains constant?

Q2. What is the molar specific heat capacity at constant volume for a solid predicted by the law of equipartition? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q3. 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 \( \gamma \)?

Q4. In a cyclic process, what is true about the change in internal energy?

Q5. Which of the following statements is incorrect about adiabatic processes?

Q6. 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 = \( 600 \, \text{J kg}^{-1} \text{K}^{-1} \))

Q7. What happens to the internal energy of a system when work is done on it in an adiabatic process?

Q8. Which of the following correctly describes irreversible processes?

Q9. 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 \( \gamma \)?

Q10. How many joules are equivalent to \( 500 \, \text{cal} \) of heat? (1 cal = \( 4.186 \, \text{J} \))