Question

$1kg$ of a diatomic gas is at a pressure of $8\times 10^{4}N/m^2$ . The density of the gas is $4kg/m^3$ , what is the energy of the gas due to its thermal motion?

• A. $3\times 10^{4}J$
• B. $5\times 10^{4}J$
• C. $6\times 10^{4}J$
• D. $7\times 10^{4}J$

Answer 1

Answer: (B)

Thermal energy correspond to internal energy
Mass $=1kg$
Density $=4kg/m^3$
$\Rightarrow$ Volume $=\frac{\text{Mass}}{\text{Density}}=\frac{1}{4}{m}^3$
Pressure $=8\times 10^{4}N-m^2$
$\therefore$ Internal energy (for diatomic gas) $f=5$
$=\frac{5}{2}p\times V=5\times 10^{4}J$
$[\because u=\frac{1}{2}fRT=\frac{1}{2}fpV$
where, $f$ is degree of freedom ]