Question

# Two thermally insulated vessels 1 and 2 are filled with air at temperature (T1,T2), volumes (V1,V2) and pressure (P1,P2) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure)

A
T1+T2
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B
(T1+T2)/2
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C
T1T2P(V1+V2)P1V1T2+P2V2T1
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D
T1T2(P1V1+P2V2)P1V1T2+P2V2T1
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Solution

## The correct option is C T1T2P(V1+V2)P1V1T2+P2V2T1From ideal gas law,P1V1=n1RT1P2V2=n2RT2Since the total mass of the gas remains same before and after the vessels are joined,n1+n2=n⟹P1V1RT1+P2V2RT2=P(V1+V2)RT⟹T=T1T2P(V1+V2)P1V1T2+P2V2T1

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