In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve is in closed position, states of the box 1 and 2 , respectively, are ( 1 atm , V , T ) and (

Question

In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve is in closed position, states of the box 1 and 2 , respectively, are ( 1 $atm, V, T$ )

and ( $0.5 atm, 4 V, T$ ). When the valve is opened, the final pressure (in atm ) of the system is P , then find the value of 10 P .

TestHub · Accepted Answer

After opening of at equilibrium temperature and pressure of whole gas is $T_{1}$ and $P_{1}$

$\displaylines n_{1} = \frac{1 \times V}{RT}, n_{2} = \frac{0.5 \times V \times 4}{RT}$

$n_{1} + n_{2} = n$ $\frac{V}{RT} + \frac{V \times 4}{2 RT} = \frac{5 VP _{1}}{RT _{1}}$

$\frac{3 V}{RT} = \frac{5 VP _{1}}{RT _{1}}; \frac{P _{1}}{T _{1}} = \frac{0.6}{T}$

$Δ Q = 0, Δ W = 0$

$∴ Δ U = 0$

$n_{1} C_{V} T + n_{2} C_{V} T = (n_{1} + n_{2}) C_{V} T_{1}$

$T_{1} = T$

$\frac{P _{1}}{T} = \frac{0.6}{T}$

$P_{1} = 0.60 atm \Rightarrow 10 P = 6$ .

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