JEE MAIN - Physics (2002 - No. 38)
1 mole of a gas with $$\gamma = 7/5$$ is mixed with $$1$$ mole of a gas with $$\gamma = 5/3,$$ then the value of $$\gamma $$ for the resulting mixture is
$$7/5$$
$$2/5$$
$$3/2$$
$$12/7$$
Explanation
$${{{n_1} + {n_2}} \over {\gamma - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}$$
$${{1 + 1} \over {\gamma - 1}} = {1 \over {{7 \over 5} - 1}} + {1 \over {{5 \over 3} - 1}}$$
$$\therefore$$ $${2 \over {\gamma - 1}} = {5 \over 2} + {3 \over 2} = 4$$
$$\therefore$$ $$2 = 4\gamma - 4 \Rightarrow \gamma = {6 \over 4} = {3 \over 2}$$
$${{1 + 1} \over {\gamma - 1}} = {1 \over {{7 \over 5} - 1}} + {1 \over {{5 \over 3} - 1}}$$
$$\therefore$$ $${2 \over {\gamma - 1}} = {5 \over 2} + {3 \over 2} = 4$$
$$\therefore$$ $$2 = 4\gamma - 4 \Rightarrow \gamma = {6 \over 4} = {3 \over 2}$$
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