First slide

laws

Question

Two spherical vessel of equal volume, are connected by a narrow tube. The apparatus contains an ideal gas at one atmosphere and 300 K. Now if one vessel is immersed in a bath of constant temperature 600K and the other in a bath of constant temperature 300 K. Then the common pressure will be

Moderate

A

1 atm
B

$\frac{4}{5} atm$
C

$\frac{4}{3} atm$
D

$\frac{3}{4} atm$

Solution

$μ = μ_{1} + μ_{2}$
$\frac{P (2 V)}{{RT}_{1}} = \frac{P^{'} v}{{RT}_{1}} + \frac{P^{'} V}{{RT}_{2}} \Rightarrow \frac{2 P}{{RT}_{1}} = \frac{P^{'}}{R} [\frac{T_{2} + T_{1}}{T_{1} T_{2}}]$
$P^{'} = \frac{2 {PT}_{2}}{(T_{1} + T_{2})} = \frac{2 \times 1 \times 600}{(300 + 600)} = \frac{4}{3} atm$

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