NEET Thermodynamics — Set 24

Question 1

In an isobaric process, $ 1.1 \, \text{moles} $ of an ideal gas expand from $ 7 \, \text{L} $ to $ 14 \, \text{L} $ at $ 390 \, \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 $. $ \Delta V = 14 - 7 = 7 \, \text{L} $. $ P = \frac{\mu R T}{V_1} = \frac{1.1 \times 8.3 \times 390}{7} = 509.01 \, \text{atm} $ (unit correction needed). Directly: $ W = \mu R T \left(\frac{V_2 - V_1}{V_1}\right) $, but $ W = P \Delta V $. $ W = 1.1 \times 8.3 \times 390 = 3560.7 \, \text{J} \approx 3561 \, \text{J} $ (adjusted).

Question 2

In an isobaric process, $ 0.5 \, \text{moles} $ of gas expand from $ 300 \, \text{K} $ to $ 450 \, \text{K} $. What is the heat supplied if $ C_p = 29.1 \, \text{J mol}^{-1} \text{K}^{-1} $?

Accepted Answer

$ \Delta Q = \mu C_p \Delta T $. $ \mu = 0.5 $, $ C_p = 29.1 $, $ \Delta T = 450 - 300 = 150 $. $ \Delta Q = 0.5 \times 29.1 \times 150 = 2182.5 \, \text{J} $.

Question 3

Which of the following statements is correct about a reversible process?

Accepted Answer

A reversible process can be reversed, restoring the system and surroundings to their original states without net external changes, requiring quasi-static conditions and no dissipation. Option D is correct.

NEET Physics: Thermodynamics — Practice Set 24

Q1. In an isobaric process, \( 1.1 \, \text{moles} \) of an ideal gas expand from \( 7 \, \text{L} \) to \( 14 \, \text{L} \) at \( 390 \, \text{K} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q2. In an isobaric process, \( 0.5 \, \text{moles} \) of gas expand from \( 300 \, \text{K} \) to \( 450 \, \text{K} \). What is the heat supplied if \( C_p = 29.1 \, \text{J mol}^{-1} \text{K}^{-1} \)?

Q3. Which of the following statements is correct about a reversible process?

Q4. A monatomic ideal gas undergoes an adiabatic expansion, reducing its temperature from \( 400 \, \text{K} \) to \( 300 \, \text{K} \). How much work is done by the gas if \( \mu = 1 \, \text{mole} \) and \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \)? (\( \gamma = 1.67 \))

Q5. How many calories are equivalent to \( 1674 \, \text{J} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

Q6. A gas at \( 11 \, \text{atm} \) and \( 90^\circ \text{C} \) in a \( 10 \, \text{L} \) container is cooled isochorically to \( 30^\circ \text{C} \). What is the final pressure?

Q7. In an adiabatic process, what compensates for the absence of heat transfer?

Q8. A system absorbs \( 730 \, \text{J} \) of heat and performs \( 190 \, \text{J} \) of work. What is the change in internal energy?

Q9. A gas at \( 10 \, \text{atm} \) and \( 80^\circ \text{C} \) in a \( 8 \, \text{L} \) container is heated isochorically to \( 140^\circ \text{C} \). What is the final pressure?

Q10. A gas undergoes an adiabatic expansion from \( 28 \, \text{L} \) to \( 84 \, \text{L} \), reducing its pressure from \( 15 \, \text{atm} \) to \( 3 \, \text{atm} \). What is the value of \( \gamma \)?