Question

$ {{C}_{V}} $ and $ {{C}_{P}} $ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then, (1) $ {{C}_{V}}-{{C}_{P}} $ larger for a diatomic ideal gas than for a monoatomic ideal gas (2) $ {{C}_{P}}+{{C}_{V}} $ is larger for a diatomic ideal gas than for a monoatomic ideal gas (3) $ \frac{{{C}_{P}}}{{{C}_{V}}} $ is larger for a diatomic ideal gas than for a monoatomic ideal gas (4) $ {{C}_{P}}.{{C}_{V}} $ is larger for a diatomic ideal gas than for a monoatomic ideal gas

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (C)

For monoatomic gas, $ {{C}_{p}}=\frac{5}{2}R $
and $ {{C}_{V}}=\frac{3}{2}R $
For diatomic gas, $ {{C}_{P}}=\frac{7}{2}R $
and $ {{C}_{V}}=\frac{5}{2}R $