Question

600 J of heat is added to a monatomic gas in a process in which the gas performs a work of 150 J. The molar heat capacity for the process is

• A. 3 R
• B. 4 R
• C. 2 R
• D. 6 R

Answer 1

Answer: (C)

2 R

Answer 2

Solution:

1. First Law of Thermodynamics:

   $$Q = \Delta U + W \implies \Delta U = Q - W = 600\,J - 150\,J = 450\,J$$

2. Internal Energy Change for Monatomic Gas:
   For a monatomic ideal gas,

   $$\Delta U = nC_V\Delta T, \quad \text{with } C_V = \frac{3}{2} R$$

   Assuming 1 mole,

   $$\Delta T = \frac{\Delta U}{C_V} = \frac{450}{\frac{3}{2} R} = \frac{450 \times 2}{3R} = \frac{900}{3R} = \frac{300}{R}$$

3. Effective Molar Heat Capacity (C):
   By definition,

   $$C = \frac{Q}{\Delta T} = \frac{600}{300/R} = \frac{600R}{300} = 2R$$