At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energ β Thermodynamics and Thermochemistry Chemistry Question
Question
At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energy by 5000 J. The molar heat capacity at constant volume is(in JK mol ) _____. . -1 -1
π‘ Solution & Explanation
**Step 1: Identify the relevant formula** For an ideal gas at constant volume, the change in internal energy is: $$\Delta U = n \cdot C_V \cdot \Delta T$$ where: - ΞU = change in internal energy - n = number of moles - C_V = molar heat capacity at constant volume - ΞT = change in temperature **Step 2: Extract given values** - n = 4 mol - Initial temperature (Tβ) = 300 K - Final temperature (Tβ) = 500 K - ΞU = 5000 J **Step 3: Calculate temperature change** $$\Delta T = T_2 - T_1 = 500 - 300 = 200 \text{ K}$$ **Step 4: Rearrange formula to solve for C_V** $$C_V = \frac{\Delta U}{n \cdot \Delta T}$$ **Step 5: Substitute values** $$C_V = \frac{5000}{4 \times 200} = \frac{5000}{800} = 6.25 \text{ J K}^{-1}\text{mol}^{-1}$$ Therefore, the answer is 6.25.