Two moles of a real gas with C_P, m = 2.5 R and a Joule-Thomson coefficient of 0

Question

Two moles of a real gas with C_P, m = 2.5 R and a Joule-Thomson coefficient of 0.266 K/bar undergo a transition from a temperature of 300. K to 500. K and a pressure of 3.0 bar to 4.0 bar. a) Calculate delta H for this process in J. b) Is there enough information given to calculate delta U (y/n), C_P, m (y/n), q (y/n), and w (y/n)? Please do not do any calculations for part b. c) In general, the temperature of this gas will increase/decrease/not change upon expansion. This question is independent of the process to which parts a and b apply.

Explanation / Answer

H= H(T,P)

dH= (dH/dT)PdT+(dH/dP)TdP, Cp=(dH/dT)P

dH= CpdT+(dH/dP)TdP (1)

but (dH/dT)P*(dT/dP)H*(dP/dH)T=-1 (2)

but uJT=joules Thomson coefficient = (dH/dP)T

hence from Eq.2, (dH/dT)P= -(dH/dT)P*(dT/dP)H=-CpuJT

hence Eq.1 becomes

dH= CPdT-CpuJTdP

when integrated

deltaH= CP*(T2-T1)-CpuJT*(P2-P1)

        = (3/2)*8.314*(500-300)- (3/2)*8.314*0.266*(4-3)

=2494.2-3.32= 2490.88 Joules
2. since deltaU= CvdT+[T*(dP/dT)V-P]dV

there is no information about CV ( not given)

cannot be calculated

work cannnot be calculated.

Cpm is given hence need not be calculated.

Q also cannot be calculated.

2. since joules thomson coefficient is +ve, the temperature of gas in general decreases with decrease in pressure. but for certain gases like H2, the decrease in pressure increases the temperature and they have -ve joule thomson coefficient.

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