19. The variation of pressure P with volume V for an
ideal monatomic gas during an adiabatic process
is shown in figure. At point A the magnitude of rate
of change of pressure with volume is
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This is an upright parabola, so the equation is P = kV 2
By Ideal gas equation,
P = nRT /V
So, nRT /V = kV 2
nRT = kV 3
By first law,
dQ = dU + PdV
Let the heat capacity of the gas in this process be C, dQ = nC dT
for diatomic gas, C v =5R /2
C= C v =5 R /2+C v = R/3 = Cv = 17R /6
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