Air in a pistoncylinder assembly is compressed from an initial state where T1 =

Question

Air in a pistoncylinder assembly is compressed from an initial state where T1 = 300 K and 1.0 bar to a final pressure of 10 bar. Assume that air behaves as an ideal gas and the process is adiabatic and internally reversible process: (a) Write down the first low and the second laws of thermodynamics for a closed system and simplify them for this problem. (b) Determine T2, in K, assuming variable specific heats (c) The work, in kJ/kg, assuming variable specific heats (d) Recalculate part (b) and (c) assuming constant specific heats

Explanation / Answer

a) first law : Q = U + W

2nd law : efficeincy of an ideal cycle = 1- T2/T1

b) T2/T1 = (P2/P1)^ (y-1)/y

for air y = 1.4

T2/300 = (10/1)^(1.4-1)/1.4

T2 = 579 K

c) work done in = Rair. (T2 - T1)/ (y-1)

   0.287 x (579 - 300) / (1.4-1)

   = 200 KJ

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