Consider a piston-cylinder assembly that contains 2.5 L of an ideal gas at 30 C

Question

Consider a piston-cylinder assembly that contains 2.5 L of an ideal gas at 30 C and 8 bar. The gas expands to 5 bar.

a) Write an energy balance for this process (you may neglect changes in potential and kinetic energy)

b) Suppose that the process is done isothermally. What is the change in internal energy, U, for the process? What is the work done, W, during the process? What is the heat transferred, Q?

c) Suppose that the process is done adiabatically (instead of isothermally), will the final temperature be greater than, equal to, or less than 30 C? Explain.

Explanation / Answer

a.) dq = du+dw

assuming dq=0

du=-dw

=> U2-U1= -d(PV)

Cv*dT = -d(PV)

and final temperature will be :

8/303= 5/T2 => T2= = -83.62500 deg. celcius

b.) In isothermal expansion

dU = 0

W = nRTln( Vb/Va) = 7.9*2.5 ln(8/5) = 9.2825 J

Q = -W = -9.2825

c.) T2<T1

since T2= T1*(P2/P1)^(r/r-1) and P2<P1

T2<30 deg.

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