Question

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

A
T1+T2
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B
(T1+T2)/2
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C
T1T2(P1V1+P2V2)P1V1T2+P2V2T1
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D
T1T2(P1V1+P2V2)P1V1T1+P2V2T2
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Solution

## The correct option is C T1T2(P1V1+P2V2)P1V1T2+P2V2T1As there is no loss of energy the initial energy is going to be equal to final energy , average kinetic energy per molecule is 32KTn1=P1V1T1 n2=P2V2T2initial KE = 32n1KT1+32n2KT2final KE = 32(n1+n2)KTSo intial KE = final KEwe get T = n1T1+n2T2n1+n2=P1V1+P2V2P1V1T1+P2V2T2=T1T2(P1V1+P2V2)P1V1T2+P2V2T1

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