NEET Thermodynamics — Set 17

Question 1

A system releases $ 670 \, \text{J} $ of heat and has $ 230 \, \text{J} $ of work done on it. What is the change in internal energy?

Accepted Answer

First Law: $ \Delta Q = \Delta U + \Delta W $. $ \Delta Q = -670 $ (heat released), $ \Delta W = -230 $ (work on system). $ -670 = \Delta U - 230 \Rightarrow \Delta U = -670 + 230 = -440 \, \text{J} $.

Question 2

A monatomic gas undergoes an adiabatic expansion from $ 820 \, \text{K} $ to $ 410 \, \text{K} $ with $ 0.9 \, \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 = 0.9 $, $ R = 8.3 $, $ T_1 = 820 $, $ T_2 = 410 $, $ \gamma = 1.67 $. $ W = \frac{0.9 \times 8.3 \times (820 - 410)}{1.67 - 1} = \frac{7.47 \times 410}{0.67} \approx 4570.15 \, \text{J} \approx 4570 \, \text{J} $.

Question 3

0.2 moles of an ideal gas at 360 K are compressed isothermally from 8 L to 2 L. What is the heat released? ($ R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} $)

Accepted Answer

Isothermal: $ \Delta U = 0 $, $ \Delta Q = \Delta W $. $ W = \mu R T \ln\left(\frac{V_2}{V_1}\right) $. $ \mu = 0.2 $, $ T = 360 $, $ V_2 = 2 $, $ V_1 = 8 $. $ W = 0.2 \times 8.3 \times 360 \times \ln\left(\frac{2}{8}\right) = 597.6 \times (-1.386) \approx -829 \, \text{J} $ (work by gas). Heat released = $ 829 \, \text{J} $.

NEET Physics: Thermodynamics — Practice Set 17

Q1. A system releases \( 670 \, \text{J} \) of heat and has \( 230 \, \text{J} \) of work done on it. What is the change in internal energy?

Q2. A monatomic gas undergoes an adiabatic expansion from \( 820 \, \text{K} \) to \( 410 \, \text{K} \) with \( 0.9 \, \text{moles} \). What is the work done? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), \( \gamma = 1.67 \))

Q3. 0.2 moles of an ideal gas at 360 K are compressed isothermally from 8 L to 2 L. What is the heat released? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q4. Which statement best describes the Second Law of Thermodynamics?

Q5. An ideal gas expands isothermally at \( 510 \, \text{K} \) from \( 8 \, \text{L} \) to \( 24 \, \text{L} \) with \( 0.2 \, \text{moles} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Q6. What thermodynamic principle explains why a bullet’s high speed does not increase its temperature?

Q7. A gas is compressed isothermally at \( 320 \, \text{K} \) releasing \( 960 \, \text{J} \) of heat. What is the work done on the gas? (\( \Delta U = 0 \))

Q8. A system absorbs 600 J of heat and does 150 J of work. What is the change in internal energy?

Q9. A gas expands adiabatically from \( 9 \, \text{atm} \) and \( 6 \, \text{L} \) to \( 3 \, \text{atm} \). What is the final volume? (\( \gamma = 1.4 \))

Q10. A system absorbs \( 850 \, \text{J} \) of heat and has \( 400 \, \text{J} \) of work done on it. What is the change in internal energy?