KVPY SX SB Exam 2018 Question Paper

Question : 23 of 120

Marks: +1, -0

For an ideal gas the internal energy is given by U = 5PV/2 + C, where C is a constant. The equation of the adiabats in the PV plane will be :-

Solution:

U=5/2PV+C

dU=5/2 PdV+5/2VdP

For adiabatic process
dU = –dW = –PdV

5/2 PdV+5/2VdP=-PdV

7/2PdV=-5/2PVdp

7PdV = –5VdP

∫7{dV}/V=∫-5{dP}/P

7 LnV = –5LnP + LnC

LnV^7 = LnP^{–5}C

V^7 = P^{–5}C

P^5V^7

= constant

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