In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :
Solution
In adiabatic process
<br><br>PV<sup>$\gamma$</sup> = constant
<br><br>$\Rightarrow$ $P{\left( {{m \over \rho }} \right)^\gamma }$ = constant
<br><br>As mass is constant
<br><br>$\therefore$ P $\propto$ ${{\rho ^\gamma }}$
<br><br>$\Rightarrow$ $${{{P_f}} \over {{P_i}}} = {\left( {{{{\rho _f}} \over {{\rho _i}}}} \right)^\gamma }$$ = ${\left( {32} \right)^{{7 \over 5}}}$ = 2<sup>7</sup> = 128
<br><br>[ For diatomic gas $\gamma$ = ${{7 \over 5}}$ ]
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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