An ideal gas is placed in a tank at 27^{circ} | vedclass

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(A) Given: Initial temperature $T_1 = 27^{\circ} C = 300 \ K$, Initial pressure $P_1 = 600 \ kPa$.After releasing one-fourth of the gas, the remaining

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$900$

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(A) Given: Initial temperature $T_1 = 27^{\circ} C = 300 \ K$, Initial pressure $P_1 = 600 \ kPa$.After releasing one-fourth of the gas, the remaining amount of gas is $n_2 = \frac{3}{4} n_1$.The volume $V$ of the tank remains constant, so $V_1 = V_2 = V$.The final temperature is $T_2 = 327^{\circ} C = 600 \ K$.Using the ideal gas law $PV = nRT$, we have $\frac{P_1 V}{n_1 T_1} = \frac{P_2 V}{n_2 T_2}$.Rearranging for $P_2$: $P_2 = P_1 	imes \left( \frac{n_2}{n_1} ight) 	imes \left( \frac{T_2}{T_1} ight)$.Substituting the values: $P_2 = 600 	imes \left( \frac{3}{4} ight) 	imes \left( \frac{600}{300} ight)$.$P_2 = 600 	imes 0.75 	imes 2 = 900 \ kPa$.

An ideal gas is placed in a tank at $27^{\circ} C$. The pressure is initially $600 \ kPa$. One fourth of the gas is then released from the tank and thermal equilibrium is established. What will be the pressure if the temperature is $327^{\circ} C$ (in $kPa$)?

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