NEET Thermodynamics — Set 5

Question 1

In a process, 300 J of heat is absorbed by a system, and 100 J of work is done on the system. What is $\Delta U$?

Accepted Answer

Using the first law: $\Delta U = q + w$. Here, $q = +300 \, \text{J}$ (heat absorbed), $w = +100 \, \text{J}$ (work done on system), so $\Delta U = 300 + 100 = 400 \, \text{J}$.

Question 2

A system absorbs 500 J of heat and performs 200 J of work. What is the change in internal energy ($\Delta U$)?

Accepted Answer

Using the first law: $\Delta U = q + w$. Here, $q = +500 \, \text{J}$ (heat absorbed), $w = -200 \, \text{J}$ (work done by system), so $\Delta U = 500 - 200 = 300 \, \text{J}$.

Question 3

What is the change in internal energy ($ \Delta U $) for the vaporization of 1 mol of water at 373 K if $ \Delta H = 40.79 \, \text{kJ/mol} $? ($ R = 8.314 \, \text{J/mol·K} $)

Accepted Answer

For $ \ce{H2O(l) \rightarrow H2O(g)} $, $ \Delta n_g = 1 $. Using $ \Delta H = \Delta U + \Delta n_g RT $, where $ RT = 8.314 \times 373 \times 10^{-3} = 3.1012 \, \text{kJ} $, we get $ \Delta U = \Delta H - \Delta n_g RT = 40.79 - 3.1012 = 37.69 \, \text{kJ/mol} $.

NEET Chemistry: Thermodynamics — Practice Set 5

Q1. In a process, 300 J of heat is absorbed by a system, and 100 J of work is done on the system. What is \(\Delta U\)?

Q2. A system absorbs 500 J of heat and performs 200 J of work. What is the change in internal energy (\(\Delta U\))?

Q3. What is the change in internal energy (\( \Delta U \)) for the vaporization of 1 mol of water at 373 K if \( \Delta H = 40.79 \, \text{kJ/mol} \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q4. A system absorbs 1200 J of heat and does 500 J of work on the surroundings at constant pressure. What is \(\Delta H\)?

Q5. Calculate \( \Delta S_{sys} \) when 1 mol of water vaporizes at 373 K. (\( \Delta H_{vap} = 40.79 \, \text{kJ/mol} \))

Q6. A system at constant pressure absorbs 1000 J of heat and expands by 0.4 L against 2.5 atm. What is \(\Delta U\)? (1 atm·L = 101.3 J)

Q7. Calculate \(\Delta H\) for \(CH_4(g) \rightarrow C(g) + 4H(g)\) using: \(\Delta H_f^\circ (CH_4,g) = -74.8 \, \text{kJ/mol}\), \(\Delta H_a (C,g) = 715 \, \text{kJ/mol}\), \(\Delta H_a (H,g) = 218 \, \text{kJ/mol}\).

Q8. Calculate \(\Delta G^\circ\) for a reaction with \(K = 2.5 \times 10^{-3}\) at 298 K. (\(R = 8.314 \, \text{J/mol·K}\))

Q9. What is the work done when 2 mol of an ideal gas expands isothermally and reversibly from 5 L to 10 L at 300 K? (\(R = 8.314 \, \text{J/mol·K}\))

Q10. For an ideal gas (\(\gamma = 1.33\)) expanding adiabatically from 8 L to 16 L at 500 K, what is the final temperature?