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12.Kinetic Theory of Gases
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$1\,kg$ of a diatomic gas is at a pressure of $8\times10^4\, N/m^2$. The density of the gas is $4\, kg/m^3$. What is the energy of the gas due to its thermal motion
A
$3\times10^4\, J$
B
$5\times10^4\, J$
C
$6\times10^4\, J$
D
$7\times10^4\, J$
Solution
For $1\, kg$ gas energy, $E=\frac{1}{2} \mathrm{RT}$
As $P=\rho r$ T there fore $R T=P / \rho$
$\begin{array}{ll}{\mathrm{E}=\frac{5}{2} \times \frac{8 \times 10^{4}}{4}} & {[\mathrm{f}=5 \text { for diatomic gas }]} \\ {\mathrm{E}=5 \times 10^{4} \text { Joule }}\end{array}$
Standard 11
Physics
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