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The pressure and density of a diatomic gas(\gamma=7 / 5) change adiabatically form \mathrm{\left(p_1, d_1\right) \text { to }\left(p_2, d_2\right) \text {. If } \frac{d_2}{d_1}=32 \text {, then } \frac{p_2}{p_1} \text { is }}

 

Option: 1

\frac{1}{128}


Option: 2

32


Option: 3

128


Option: 4

256


Answers (1)

best_answer

\mathrm{p^{V^\gamma}=\text { constant. For a given mass of gas, } V \propto \frac{1}{d}}

Hence

\mathrm{\frac{p}{d^\gamma}=\text { constant }}

\mathrm{\begin{aligned} & \therefore \frac{p_1}{d_1^\gamma}=\frac{p_2}{d_2^\gamma} \\ & \text { Or } \frac{p_2}{p_1}=\left(\frac{d_2}{d_1}\right)^\gamma=(32)^{7 / 5}=(2)^7=128 \end{aligned}}

Posted by

Suraj Bhandari

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