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Question

If 2 moles of an ideal monoatomic gas at temperature T0 is mixed with 4 moles of another ideal monoatomic gas at temperature 2T0, then the temperature of the mixture is

A
53T0
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B
32T0
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C
43T0
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D
54T0
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Solution

The correct option is A 53T0
For the internal energy of mixture,
Umix=(n1+n2)fRT2
Degree of freedom f will be same for both gases and the mixture as gases mixed are monoatomic.
For the mixture we can apply,
Umix=U1+U2
(n1+n2)fRT2=n1fRT02+n2fR×2T02
(n1+n2)T=n1T0+2n2T0
(2+4)T=2T0+8T0
T=10T06=53T0

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