Two samples of gas A and B are initially at t | vedclass

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(C) For an isothermal process,the relationship between pressure and volume is given by $P_1 V_1 = P_2 V_2$. Given $V_1 = V$ and $V_2 = V/2$,we have $P

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Less than the final pressure of $B$

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(C) For an isothermal process,the relationship between pressure and volume is given by $P_1 V_1 = P_2 V_2$. Given $V_1 = V$ and $V_2 = V/2$,we have $P_A = P_0 (V / (V/2)) = 2 P_0$.For an adiabatic process,the relationship is given by $P_1 V_1^\gamma = P_2 V_2^\gamma$. Given $V_1 = V$ and $V_2 = V/2$,we have $P_B = P_0 (V / (V/2))^\gamma = 2^\gamma P_0$.Since for any gas $\gamma > 1$,it follows that $2^\gamma > 2$.Therefore,the final pressure of $B$ $(P_B = 2^\gamma P_0)$ is greater than the final pressure of $A$ $(P_A = 2 P_0)$.Thus,the final pressure of $A$ is less than the final pressure of $B$.

Process	Condition
$(I)$ Adiabatic	$(A) \Delta W = 0$
$(II)$ Isothermal	$(B) \Delta Q = 0$
$(III)$ Isochoric	$(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D) \Delta U = 0$

Two samples of gas $A$ and $B$ are initially at the same pressure and temperature. They are compressed from volume $V$ to $V/2$. If $A$ is compressed isothermally and $B$ is compressed adiabatically,then the final pressure of $A$ is:

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