Question 98: Thermodynamics & KTG

Question

$$C_V$$ and $$C_P$$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

Accepted Answer

We know that $${C_P} - {C_V} = R$$ is same for all gases. For a diatomic gas, we have
$${C_V} = {{5R} \over 2}$$
Therefore, $${C_P} = {C_V} + R = {{7R} \over 2}$$
For a monoatomic gas, we have
$${C_V} = {{3R} \over 2}$$
$${C_P} = {{5R} \over 2}$$
Therefore,
$${C_P} + {C_V} = 6R$$ (diatomic)
$${C_P} + {C_V} = 4R$$ (monoatomic)
$${{{C_P}} \over {{C_V}}} = {7 \over 5} = 1.4$$ (diatomic)
$${{{C_P}} \over {{C_V}}} = {5 \over 3} = 1.67$$ (monoatomic)
$${C_P}\,.\,{C_V} = {{35{R^2}} \over 4}$$ (diatomic)
$${C_P}\,.\,{C_V} = {{15{R^2}} \over 4}$$ (monoatomic)

Answer

$$C_P-C_V$$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.

Answer

$$C_P+C_V$$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.

Answer

$$C_P/C_V$$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.

Answer

$$C_P~.C_V$$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.

Thermodynamics & KTG

C_V and C_P$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

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