If the degree of freedom of a gas is $f,$ then the ratio of two specific heats ${C_P}/{C_V}$ is given by

  • A
    $1 + \frac{2}{f}$
  • B
    $1 - \frac{2}{f}$
  • C
    $1 + \frac{1}{f}$
  • D
    $1 - \frac{1}{f}$

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What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

The molar specific heat at constant pressure of an ideal gas is $(7/2)R$. The ratio of specific heat at constant pressure to that at constant volume is

The quantity of heat required to raise the temperature of one mole of a monoatomic gas by one degree Kelvin at constant volume is

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.

$C_{v}$ and $C_{p}$ denote the molar specific heat capacities of a gas at constant volume and constant pressure,respectively. Then
$(A)$ $C_{p}-C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
$(B)$ $C_{p}+C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
$(C)$ $C_{p} / C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
$(D)$ $C_{p} \cdot C_v$ is larger for a diatomic ideal gas than for a monoatomic ideal gas

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