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Question

An ideal gas undergoes an adiabatic process obeying the relation PV4/3=constant. If its initial temperature is 300K and then its pressure is increased up to four times its initial value, then the final temperature is:

A
3002
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B
30032
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C
600
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D
1200
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Solution

The correct option is B 3002
Let P1, V1 and T1 be the initial pressure, initial volume and inital temprrature respectively and P2, V2 and T2 be the final pressure, final volume and final temprrature respectively.

PV4/3=constant

V2=V1(P1P2)34.

But P2=4P1.

V2=V1(14)34

Also, PV=nRT

Hence, 4P1V1(14)34=nRT2

T2=4(12)32=nRT2

Thus, T2=2T1=3002.

Hence, the correct answer is option A.

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