JEE MAIN - Physics (2004 - No. 56)
One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gamma = 7/5} \right)$$. What is $$\gamma $$ for the mixture? $$\gamma $$ Denotes the ratio of specific heat at constant pressure, to that at constant volume
$$35/23$$
$$23/15$$
$$3/2$$
$$4/3$$
Explanation
$${{{n_1} + {n_2}} \over {\gamma - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}$$
$$ \Rightarrow {{1 + 1} \over {\gamma - 1}}$$
$$ = {1 \over {{5 \over 3} - 1}} + {1 \over {{7 \over 5} - 1}}$$
$$ \Rightarrow \gamma = {3 \over 2}$$
$$ \Rightarrow {{1 + 1} \over {\gamma - 1}}$$
$$ = {1 \over {{5 \over 3} - 1}} + {1 \over {{7 \over 5} - 1}}$$
$$ \Rightarrow \gamma = {3 \over 2}$$
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