JEE MAIN - Physics (2020 - 7th January Morning Slot - No. 12)
Two moles of an ideal gas with $${{{C_P}} \over {{C_V}}} = {5 \over 3}$$
are mixed with 3 moles of another ideal gas
with $${{{C_P}} \over {{C_V}}} = {4 \over 3}$$. The value of $${{{C_P}} \over {{C_V}}}$$ for the
mixture is :
1.50
1.45
1.47
1.42
Explanation
Cp = $${{{n_1}{C_{{p_1}}} + {n_2}{C_{{p_2}}}} \over {{n_1} + {n_2}}}$$
Cv = $${{{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}} \over {{n_1} + {n_2}}}$$
$$\gamma $$mix = $${{{C_p}} \over {{C_v}}}$$ = $${{2 \times {5 \over 2}R + 3 \times {8 \over 2}R} \over {2 \times {3 \over 2}R + 3 \times {6 \over 2}R}}$$
= $${{5 + 12} \over {3 + 9}}$$ = 1.42
Cv = $${{{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}} \over {{n_1} + {n_2}}}$$
$$\gamma $$mix = $${{{C_p}} \over {{C_v}}}$$ = $${{2 \times {5 \over 2}R + 3 \times {8 \over 2}R} \over {2 \times {3 \over 2}R + 3 \times {6 \over 2}R}}$$
= $${{5 + 12} \over {3 + 9}}$$ = 1.42
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