Question

$ 1\,kg $ of a diatomic gas is at a pressure of $ 8 \times 10^4 \,N/m^ 2 $ . The density of the gas is $ 4 \,kg/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 $= 1 \,kg$
Density $= 4 \,kg/m^3$
$\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 ]