NEET Thermodynamics — Set 1

Question 1

A gas is compressed adiabatically, increasing its pressure from $ 1 \, \text{atm} $ to $ 4 \, \text{atm} $ in a $ 10 \, \text{L} $ container. What is the final volume? ($ \gamma = 1.6 $)

Accepted Answer

$ P_1 V_1^\gamma = P_2 V_2^\gamma $. $ 1 \times 10^{1.6} = 4 \times V_2^{1.6} $. $ V_2^{1.6} = \frac{10^{1.6}}{4} $. $ V_2 = \left(\frac{10^{1.6}}{4}\right)^{1/1.6} = 10 \times 4^{-1/1.6} $. $ 4^{-0.625} \approx 0.315 $, $ V_2 \approx 10 \times 0.315 \approx 3.15 \, \text{L} $.

Question 2

A monatomic gas undergoes an adiabatic expansion from $ 740 \, \text{K} $ to $ 370 \, \text{K} $ with $ 0.7 \, \text{moles} $. What is the work done? ($ R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} $, $ \gamma = 1.67 $)

Accepted Answer

$ W = \frac{\mu R (T_1 - T_2)}{\gamma - 1} $. $ \mu = 0.7 $, $ R = 8.3 $, $ T_1 = 740 $, $ T_2 = 370 $, $ \gamma = 1.67 $. $ W = \frac{0.7 \times 8.3 \times (740 - 370)}{1.67 - 1} = \frac{5.81 \times 370}{0.67} \approx 3208.96 \, \text{J} \approx 3209 \, \text{J} $.

Question 3

A gas at $ 3 \, \text{atm} $ and $ 400 \, \text{K} $ is cooled isochorically to $ 200 \, \text{K} $. What is the final pressure?

Accepted Answer

For isochoric: $ \frac{P_1}{T_1} = \frac{P_2}{T_2} $. $ P_1 = 3 $, $ T_1 = 400 $, $ T_2 = 200 $. $ \frac{3}{400} = \frac{P_2}{200} \Rightarrow P_2 = \frac{3 \times 200}{400} = 1.5 \, \text{atm} $.

NEET Physics: Thermodynamics — Practice Set 1

Q1. A gas is compressed adiabatically, increasing its pressure from \( 1 \, \text{atm} \) to \( 4 \, \text{atm} \) in a \( 10 \, \text{L} \) container. What is the final volume? (\( \gamma = 1.6 \))

Q2. A monatomic gas undergoes an adiabatic expansion from \( 740 \, \text{K} \) to \( 370 \, \text{K} \) with \( 0.7 \, \text{moles} \). What is the work done? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), \( \gamma = 1.67 \))

Q3. A gas at \( 3 \, \text{atm} \) and \( 400 \, \text{K} \) is cooled isochorically to \( 200 \, \text{K} \). What is the final pressure?

Q4. Which of the following correctly characterizes an adiabatic process?

Q5. What is the primary condition for a system to be in mechanical equilibrium?

Q6. An ideal gas expands isothermally at \( 480 \, \text{K} \) from \( 6 \, \text{L} \) to \( 18 \, \text{L} \) with \( 0.6 \, \text{moles} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q7. Which of the following statements is incorrect about an adiabatic expansion of an ideal gas?

Q8. According to the Kelvin-Planck statement, what is impossible for a heat engine?

Q9. What is the main difference between heat and internal energy in thermodynamics?

Q10. An ideal gas expands isothermally at \( 450 \, \text{K} \) from \( 4 \, \text{L} \) to \( 12 \, \text{L} \) with \( 0.3 \, \text{moles} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q11. How much heat is required to raise the temperature of \( 0.2 \, \text{kg} \) of lead from \( 50^\circ \text{C} \) to \( 80^\circ \text{C} \)? (Specific heat of lead = \( 127.7 \, \text{J kg}^{-1} \text{K}^{-1} \))

Q12. In an isothermal compression of an ideal gas, what balances the work done on the system?

Q13. In an isobaric process, \( 1.5 \, \text{moles} \) of an ideal gas expand from \( 9 \, \text{L} \) to \( 15 \, \text{L} \) at \( 380 \, \text{K} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q14. In an isochoric process, what is the primary effect of heat addition?

Q15. A gas undergoes an adiabatic expansion from \( 22 \, \text{L} \) to \( 66 \, \text{L} \), reducing its pressure from \( 12 \, \text{atm} \) to \( 2 \, \text{atm} \). What is the value of \( \gamma \)?