NEET Thermodynamics — Set 15

Question 1

In an isobaric process, $ 1.5 \, \text{moles} $ of an ideal gas expand from $ 5 \, \text{L} $ to $ 15 \, \text{L} $ at $ 300 \, \text{K} $. What is the work done by the gas? ($ R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} $)

Accepted Answer

$ W = P \Delta V $, $ P V = \mu R T $. Initial $ P = \frac{\mu R T}{V_1} = \frac{1.5 \times 8.3 \times 300}{5} = 747 \, \text{atm} $ (unit adjustment needed). Correctly: $ W = \mu R T \left(\frac{V_2 - V_1}{V_1}\right) $, but simply $ W = P \Delta V $. $ \Delta V = 15 - 5 = 10 \, \text{L} $, adjust units: $ W = \mu R T \left(\frac{\Delta V}{V_1}\right) \times \text{pressure factor} $. Direct: $ W = \mu R \Delta T $, but $ T $ constant, so $ W = P \Delta V $, use $ \mu R T $. $ W = 1.5 \times 8.3 \times 300 \times \frac{10}{5} = 7470 \, \text{J} $ (adjusted for consistency).

Question 2

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

Accepted Answer

Work ($ W = P \Delta V $) is path-dependent, not a state variable, and involves mechanical energy transfer, not temperature differences (unlike heat). Option C is incorrect.

Question 3

Why does the specific heat capacity of a gas differ at constant pressure and constant volume?

Accepted Answer

At constant pressure ($ C_p $), heat supplies energy for both internal energy increase and work done due to expansion ($ \Delta Q = \Delta U + P \Delta V $). At constant volume ($ C_v $), no work is done ($ \Delta V = 0 $), so heat only increases internal energy ($ \Delta Q = \Delta U $). Thus, $ C_p > C_v $, and $ C_p - C_v = R $.

NEET Physics: Thermodynamics — Practice Set 15

Q1. In an isobaric process, \( 1.5 \, \text{moles} \) of an ideal gas expand from \( 5 \, \text{L} \) to \( 15 \, \text{L} \) at \( 300 \, \text{K} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q2. Which of the following statements is incorrect about work in thermodynamics?

Q3. Why does the specific heat capacity of a gas differ at constant pressure and constant volume?

Q4. In a thermodynamic process, what indicates that a variable is not in equilibrium?

Q5. A gas expands adiabatically from \( 8 \, \text{atm} \) and \( 16 \, \text{L} \) to \( 2 \, \text{atm} \). What is the final volume? (\( \gamma = 1.5 \))

Q6. A gas undergoes an adiabatic compression from \( 18 \, \text{L} \) to \( 6 \, \text{L} \), increasing its pressure from \( 4 \, \text{atm} \) to \( 12 \, \text{atm} \). What is the value of \( \gamma \)?

Q7. How much heat is required to raise the temperature of \( 0.4 \, \text{kg} \) of tungsten from \( 40^\circ \text{C} \) to \( 70^\circ \text{C} \)? (Specific heat of tungsten = \( 134.4 \, \text{J kg}^{-1} \text{K}^{-1} \))

Q8. Which of the following correctly describes the First Law of Thermodynamics?

Q9. In an isobaric process, \( 0.6 \, \text{moles} \) of gas expand from \( 400 \, \text{K} \) to \( 480 \, \text{K} \). What is the heat supplied if \( C_p = 25.0 \, \text{J mol}^{-1} \text{K}^{-1} \)?

Q10. What is the significance of the \( P-V \) relationship in an adiabatic process for an ideal gas?