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 :
Solution
C<sub>p</sub> = ${{{n_1}{C_{{p_1}}} + {n_2}{C_{{p_2}}}} \over {{n_1} + {n_2}}}$
<br><br>C<sub>v</sub> = ${{{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}} \over {{n_1} + {n_2}}}$
<br><br>$\gamma$<sub>mix</sub> = ${{{C_p}} \over {{C_v}}}$ = $${{2 \times {5 \over 2}R + 3 \times {8 \over 2}R} \over {2 \times {3 \over 2}R + 3 \times {6 \over 2}R}}$$
<br><br>= ${{5 + 12} \over {3 + 9}}$ = 1.42
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
This question is part of PrepWiser's free JEE Main question bank. 271 more solved questions on Thermodynamics are available — start with the harder ones if your accuracy is >70%.