In this problem you will follow a piston around a cycle, a series of processes t

ID: 2993827 • Letter: I

Question

In this problem you will follow a piston around a cycle, a series of processes that end up

where they began. We'll cover these much more later on, but you can begin to think about

how thermodynamic processes can be strung together to do useful things for us.

a)A piston undergoes a process where the polytropic relation P1:2 = const holds true.

If the piston is lled with 1kg of ideal air at 30C and 1atm initially, and is compressed

until the volume is halved, what is the nal pressure of the air? How much work was done?

b)This same piston is then allowed to cool down to 30C. How much heat was trans-

ferred out of the system in this process?

PV^1.2 = constant

V2 = 1/2*V1

P1*V1^1.2 = P2*V2^1.2

P2 = P1*(V1/V2)^1.2

P2 = 2.3 atm

n = m/M = 1000/28.9 = 34.6

P1*V1 = n*R*T

1*10^5 *V1 = 34.6*8.314*303

V1 = 0.872 m^3

V2 =0.5*V1 = 0.436

Work in polytropic process

W = (P2*V2 - P1*V1)/(1-n) = (2.3*0.436-1*0.872)*10^5/(1-1.2)

W = -65.22 kJ

P1*V1/T1 = P2*V2/T2

T2 = T1*(P2*V2/P1*V1)=348.45 K = 75.45 deg

Change in internal enegry from 2 to 1

dU = n*Cv*dT = 34.6*0.718*(30-75.45) = -1129.1 kJ

work done from 2 to 1

W = 65.22 kJ

dQ = dU + W

dQ = -1063.89kJ

Heat released from system = 1063.89 kJ

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.