Question

1. A piston cylinder device contains 5 kg nitrogen.  The pressure inside the system is 100 kPa, and the temperature is 17^oC.  The relationship between pressure and volume is    PV³ = C.  If a process results in a volume reduction of 2x, calculate the work and heat transfer occurring during the process.

Answer 1

Piston cylinder device contains mass of N2, m = 5 kg

Number of moles, n = 5000gm/(28 gm/mol ) = 178.57 mol

Pressure inside the system, P = 100 kPa

Temperature T = 17 C

PV³ = const

Initial volume V1 = V1

Volume reduction V2 = V1/2

PV³ = C

Put P = RT/V

RT/V * V³ = C

T1V1² = T2V2²

T2 = T1*(V1/V2)² = 300*(2)² = 1200k

Work transfer during the process,

W = nR(T1 - T2) /(n-1)

W = 178.57*8.314J/mol.k * (1200 - 300)/(3-1) = 668089.28 J = 668.08 kJ

work transfer w = 668.09 kJ

heat transfer for polytropic process ,

specific heat ratio for N2, Y = 1.4

Q = W *(Y-1)/(n-1)

Q = 668.09*(1.4 - 1)/(3-1) = 133.61 kJ