NEET Thermodynamics — Set 14

Question 1

A gas at $ 9 \, \text{atm} $ and $ 70^\circ \text{C} $ in a $ 6 \, \text{L} $ container is cooled isochorically to $ 10^\circ \text{C} $. What is the final pressure?

Accepted Answer

For isochoric: $ \frac{P_1}{T_1} = \frac{P_2}{T_2} $. $ P_1 = 9 \, \text{atm} $, $ T_1 = 70 + 273 = 343 \, \text{K} $, $ T_2 = 10 + 273 = 283 \, \text{K} $. $ \frac{9}{343} = \frac{P_2}{283} \Rightarrow P_2 = \frac{9 \times 283}{343} \approx 7.42 \, \text{atm} $.

Question 2

A gas at $ 1 \, \text{atm} $ and $ 300 \, \text{K} $ in a $ 10 \, \text{L} $ container is heated isobarically to $ 600 \, \text{K} $. What is the work done by the gas? ($ R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} $)

Accepted Answer

For isobaric: $ W = P \Delta V $. Initial: $ P V_1 = \mu R T_1 \Rightarrow 1 \times 10 = \mu \times 8.3 \times 300 \Rightarrow \mu = \frac{10}{2490} \approx 0.004 \, \text{moles} $. Final: $ V_2 = \frac{\mu R T_2}{P} = \frac{0.004 \times 8.3 \times 600}{1} = 19.92 \, \text{L} $. $ \Delta V = 19.92 - 10 \approx 9.92 \, \text{L} $. $ W = P \Delta V = 1 \times 9.92 \times 101325 \, \text{Pa} \times 10^{-3} \, \text{m}^3 = 1004.8 \, \text{J} \approx 1005 \, \text{J} $ (converted units).

Question 3

Which of the following statements is incorrect about an adiabatic process?

Accepted Answer

In an adiabatic process ($ \Delta Q = 0 $), temperature can change (e.g., decreases during expansion), as internal energy adjusts via work ($ \Delta U = -\Delta W $). Option B is incorrect as temperature is not constant.

NEET Physics: Thermodynamics — Practice Set 14

Q1. A gas at \( 9 \, \text{atm} \) and \( 70^\circ \text{C} \) in a \( 6 \, \text{L} \) container is cooled isochorically to \( 10^\circ \text{C} \). What is the final pressure?

Q2. A gas at \( 1 \, \text{atm} \) and \( 300 \, \text{K} \) in a \( 10 \, \text{L} \) container is heated isobarically to \( 600 \, \text{K} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q3. Which of the following statements is incorrect about an adiabatic process?

Q4. A system releases \( 600 \, \text{J} \) of heat and performs \( 250 \, \text{J} \) of work. What is the change in internal energy?

Q5. A gas is compressed adiabatically from \( 24 \, \text{L} \) to \( 6 \, \text{L} \), increasing its pressure from \( 5 \, \text{atm} \) to \( 20 \, \text{atm} \). What is \( \gamma \)?

Q6. Which of the following statements is incorrect about a cyclic process?

Q7. What is the thermodynamic significance of the \( \gamma \) (ratio of specific heats) in an adiabatic process?

Q8. In an adiabatic process, a gas expands from a volume of \( 1 \, \text{L} \) to \( 4 \, \text{L} \), reducing its pressure from \( 16 \, \text{atm} \) to \( 1 \, \text{atm} \). What is the value of \( \gamma \) (ratio of specific heats)?

Q9. How much heat is required to convert \( 1 \, \text{g} \) of water from liquid at \( 100^\circ \text{C} \) to vapor at \( 100^\circ \text{C} \) at \( 1 \, \text{atm} \)? (Latent heat = \( 2256 \, \text{J/g} \))

Q10. What is the molar specific heat capacity at constant pressure for a monatomic gas if \( C_v = 12.45 \, \text{J mol}^{-1} \text{K}^{-1} \) and \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \)?