NEET Thermodynamics — Set 12

Question 1

What is the primary implication of the First Law of Thermodynamics?

Accepted Answer

The First Law of Thermodynamics is a statement of energy conservation: $ \Delta Q = \Delta U + \Delta W $. It implies that the total energy supplied to a system (as heat) equals the increase in internal energy plus the work done by the system.

Question 2

An ideal gas expands isothermally at $ 540 \, \text{K} $ from $ 10 \, \text{L} $ to $ 30 \, \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} $)

Accepted Answer

For isothermal: $ W = \mu R T \ln\left(\frac{V_2}{V_1}\right) $. $ \mu = 0.3 $, $ R = 8.3 $, $ T = 540 $, $ V_2 = 30 $, $ V_1 = 10 $. $ W = 0.3 \times 8.3 \times 540 \times \ln\left(\frac{30}{10}\right) = 1344.6 \times \ln(3) $. $ \ln(3) \approx 1.0986 $, $ W \approx 1344.6 \times 1.0986 \approx 1477 \, \text{J} $.

Question 3

A gas at 4 atm and 300 K in a 5 L container is compressed isothermally to 2 L. What is the work done on the gas? ($ R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} $)

Accepted Answer

Isothermal: $ W = \mu R T \ln\left(\frac{V_2}{V_1}\right) $. $ P_1 V_1 = \mu R T \Rightarrow 4 \times 5 = \mu \times 8.3 \times 300 \Rightarrow \mu = \frac{20}{2490} \approx 0.008 \, \text{mol} $. $ W = 0.008 \times 8.3 \times 300 \times \ln\left(\frac{2}{5}\right) = 19.92 \times (-0.916) \approx -18.25 \, \text{J} $ (work by gas negative). Work on gas = $ 18.25 \, \text{J} \approx 18 \, \text{J} $.

NEET Physics: Thermodynamics — Practice Set 12

Q1. What is the primary implication of the First Law of Thermodynamics?

Q2. An ideal gas expands isothermally at \( 540 \, \text{K} \) from \( 10 \, \text{L} \) to \( 30 \, \text{L} \) with \( 0.3 \, \text{moles} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q3. A gas at 4 atm and 300 K in a 5 L container is compressed isothermally to 2 L. What is the work done on the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q4. How many calories are equivalent to \( 2093 \, \text{J} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

Q5. A diatomic gas undergoes an adiabatic expansion from \( 860 \, \text{K} \) to \( 430 \, \text{K} \) with \( 0.5 \, \text{moles} \). What is the work done? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), \( \gamma = 1.4 \))

Q6. A system in a cyclic process absorbs \( 980 \, \text{J} \) of heat and performs \( 420 \, \text{J} \) of work. What is the heat rejected?

Q7. A system absorbs \( 920 \, \text{J} \) of heat and performs \( 280 \, \text{J} \) of work. What is the change in internal energy?

Q8. What is the change in internal energy when \( 1 \, \text{mole} \) of an ideal gas is heated from \( 300 \, \text{K} \) to \( 350 \, \text{K} \) at constant volume? (\( C_v = 20.8 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q9. A system releases \( 790 \, \text{J} \) of heat and has \( 310 \, \text{J} \) of work done on it. What is the change in internal energy?

Q10. A system absorbs \( 800 \, \text{J} \) of heat and has \( 350 \, \text{J} \) of work done on it. What is the change in internal energy?