Thermodynamics problem Nitrogen gas is expanded in a polytropic process with m =
ID: 1408438 • Letter: T
Question
Thermodynamics problem
Nitrogen gas is expanded in a polytropic process with m = 1.45 from 2 MPa and 1200 K to 200 kPa in a piston-cylinder device. (a)Write down the mathematical relationship between pressure and volume for this process. (b)Calculate the molar volume of the gas after expansion in m^3/mol. (c)Work out the temperature of the nitrogen gas (in Kelvin) after the expansion. (d)How much work is produced during the expansion process, in kJ/kg? expressed as nR/m -1 [T_2 - T_1], where n is the number of moles of nitrogen gas. The rest of the symbols have their usual meaning. Show all your working clearly - and legibly if you're handwriting your submission.Explanation / Answer
According to the problem,
As it is a polytropic process and given m = n =1.45, P1 = 2 * 106 Pa , T1 = 1200K, P2 = 0.2 * 106 Pa.
a) The mathematical expression for a polytropic process is,
PVm = C where C is contant m = 1.45
PV1.45 = C
b)First calculate the molar volume of the nitrogen gas,
PV = nRT as it is a idela gas
P1V1 = n R T1
V1/n = RT1/P1
V1/n = 8.314 *1200/ 2 * 106
V1/n = 5* 10-3 m3/mol
Now, calculate the final molar volume of nitrogen,
P1V1n1.45 = P2V2/n1.45
V2/n1.45 = P1V1/n1.45 /P2
V2/n1.45 = 2 * 106* (5.0 * 10-3)1.45/0.2 * 106
V2/n= 24.47 * 10-3 m3/mol
c) Using ideal gas equation again to calcualte the final temparature,
P2V2 = n R T2
T2 = P2V2/ nR
T2 = 0.2 * 106 * 24.47 * 10-3/ 8.314
T2 = 587.28 K
d) Work produced during the expansion process is,
W = nR[T2 - T1]/m-1
W = (m/M)* R * [587.28 - 1200]/1.45-1
W/m = 8.314* 612.72/28* 10-3*0.45
W/m = 404.3 * 10-3J/kg
W/m = 404.3 kJ/kg
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