JEE MAIN - Physics (2009 - No. 23)
One $$kg$$ 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 ?
$$5 \times {10^4}\,J$$
$$6 \times {10^4}\,J$$
$$7 \times {10^4}\,J$$
$$3 \times {10^4}\,J$$
Explanation
$$Volume\,\, = \,\,{{mass} \over {density}} = {1 \over 4}{m^3}$$
$$K.E = {5 \over 2}PV$$
$$ = {5 \over 2} \times 8 \times {10^4} \times {1 \over 4}$$
$$ = 5 \times {10^4}J$$
$$K.E = {5 \over 2}PV$$
$$ = {5 \over 2} \times 8 \times {10^4} \times {1 \over 4}$$
$$ = 5 \times {10^4}J$$
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