NEET Thermodynamics — Set 9

Question 1

In an isobaric process, $ 0.9 \, \text{moles} $ of an ideal gas expand from $ 4 \, \text{L} $ to $ 10 \, \text{L} $ at $ 340 \, \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 = 10 - 4 = 6 \, \text{L} $. $ P = \frac{\mu R T}{V_1} = \frac{0.9 \times 8.3 \times 340}{4} = 635.55 \, \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 = 0.9 \times 8.3 \times 340 = 2540.34 \, \text{J} \approx 2540 \, \text{J} $ (adjusted).

Question 2

A gas expands adiabatically from $ 6 \, \text{atm} $ and $ 12 \, \text{L} $ to $ 2 \, \text{atm} $. What is the final volume? ($ \gamma = 1.5 $)

Accepted Answer

$ P_1 V_1^\gamma = P_2 V_2^\gamma $. $ 6 \times 12^{1.5} = 2 \times V_2^{1.5} $. $ V_2^{1.5} = \frac{6}{2} \times 12^{1.5} = 3 \times 12^{1.5} $. $ 12^{1.5} = 12 \times 12^{0.5} \approx 41.57 $, $ V_2^{1.5} = 3 \times 41.57 \approx 124.71 $. $ V_2 = (124.71)^{1/1.5} = (124.71)^{2/3} \approx 25 \, \text{L} $.

Question 3

Which statement correctly describes the concept of temperature?

Accepted Answer

Temperature measures the average kinetic energy of molecules, reflecting the system’s thermal state, and is equal in thermal equilibrium (Zeroth Law). Option A is correct.

NEET Physics: Thermodynamics — Practice Set 9

Q1. In an isobaric process, \( 0.9 \, \text{moles} \) of an ideal gas expand from \( 4 \, \text{L} \) to \( 10 \, \text{L} \) at \( 340 \, \text{K} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q2. A gas expands adiabatically from \( 6 \, \text{atm} \) and \( 12 \, \text{L} \) to \( 2 \, \text{atm} \). What is the final volume? (\( \gamma = 1.5 \))

Q3. Which statement correctly describes the concept of temperature?

Q4. How much heat is required to vaporize \( 0.8 \, \text{g} \) of water at \( 100^\circ \text{C} \) and \( 1 \, \text{atm} \)? (Latent heat = \( 2256 \, \text{J/g} \))

Q5. In thermodynamics, what does internal energy represent?

Q6. A gas is compressed adiabatically from \( 15 \, \text{L} \) to \( 5 \, \text{L} \), increasing its pressure from \( 3 \, \text{atm} \) to \( 12 \, \text{atm} \). What is \( \gamma \)?

Q7. How much heat is required to raise the temperature of \( 0.3 \, \text{kg} \) of lead from \( 35^\circ \text{C} \) to \( 65^\circ \text{C} \)? (Specific heat of lead = \( 127.7 \, \text{J kg}^{-1} \text{K}^{-1} \))

Q8. 0.4 moles of an ideal gas at 340 K expand adiabatically from 7 atm to 1 atm. If \( \gamma = 1.4 \), what is the final temperature?

Q9. What is the relationship between \( C_p \) and \( C_v \) for an ideal gas?

Q10. A gas undergoes an adiabatic expansion from \( 30 \, \text{L} \) to \( 90 \, \text{L} \), reducing its pressure from \( 9 \, \text{atm} \) to \( 1 \, \text{atm} \). What is the value of \( \gamma \)?