7 g helium at 50 kPa and 200 K (ideal gas, M = 4, k = 5/3) are compressed polytr

Question

7 g helium at 50 kPa and 200 K (ideal gas, M = 4, k = 5/3) are compressed polytropically in a quasistatic process with pv1.8 to 600 kPa.
find the final temperature of helium. find the work and heat interactions

Explanation / Answer

PV^1.8 = Constant. PV = nRT V1 = nRT1/P1 = ((7/4)*8.314*200)/(50*1000) = 0.058198 m^3 a)P1V1^1.8 = P2V2^1.8 =>V2 = ((50*1000*(0.058198^1.8))/(600*1000))^(1/1.8) = 0.014633996 m^3 P2V2 = nRT2 =>T2 = (600*1000*0.014633996)/((7/4)*8.314) = 603.4845 K b)Work Done = (P1V1-P2V2)/(n-1) = ((50*(1000)*0.058198)-(600*1000*0.014633996))/(1.8-1) = -7338.122 J Q = (W*(gamma-n))/(gamma-1) = ((-7338.122)*((5/3)-1.8))/((5/3)-1) = 1467.6244 J

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