The volume of an ideal gas (gamma=1.5) is cha | vedclass

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(C) For an adiabatic process,the relation between pressure and volume is given by $P_i V_i^\gamma = P_f V_f^\gamma$.Given: $V_i = 5 \ L$,$V_f = 4 \ L$

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$8/(5\sqrt{5})$

Vedclass · Answer

(C) For an adiabatic process,the relation between pressure and volume is given by $P_i V_i^\gamma = P_f V_f^\gamma$.Given: $V_i = 5 \ L$,$V_f = 4 \ L$,and $\gamma = 1.5 = 3/2$.Substituting the values into the equation: $P_i (5)^{3/2} = P_f (4)^{3/2}$.Rearranging to find the ratio of initial pressure to final pressure: $\frac{P_i}{P_f} = \left(\frac{4}{5}\right)^{3/2}$.Calculating the value: $\left(\frac{4}{5}\right)^{3/2} = \left(\frac{4}{5}\right) \cdot \sqrt{\frac{4}{5}} = \frac{4}{5} \cdot \frac{2}{\sqrt{5}} = \frac{8}{5\sqrt{5}}$.

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5 \ L$ to $4 \ L$. The ratio of initial pressure to final pressure is:

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