A piston cylinder assembly (volume = 0.71 m^3) contains superheated water vapor
ID: 1717988 • Letter: A
Question
A piston cylinder assembly (volume = 0.71 m^3) contains superheated water vapor under 3.0 bar of pressure at a temperature of 200 degree C. Given the parameters in the diagram illustrated, determine the: Instantaneously, a new force is applied while letting the system reject heat. The final state is now a compressed liquid under 50 bar of pressure at a temperature of 100 degree C. Calculate the: The piston and cylinder arc poor conductors and there is negligible friction between them Show all calculations and unit conversions otherwise no points will be given.Explanation / Answer
a) Mass of the water vapor is given as
n = m / W
m = nW
m = Required mass of water vapor , n = number of moles , W = molecular weight of water vapor
As molecular weight of water vapor is constant = 18g / mol
Number of moles will be found by using ideal gas equation
PV = nRT
n = PV / RT
n =( 300000 pa) (0.71m3) /( 8.13 J / mol K)(473K) 1bar = 100000pa
n = 55.38mol
Now the mass of water will be
m = nW = (55.38mol) (18g/mol) = 997.01 g
m = o.997kg
b) Applied force would be the given as
F = PA = (101325pa) (1.1)(10-2)2 = 11.14N
c) Again using ideal gas equation
PV = nRT
n = PV / RT
n = (5000000) (0.71) /( 8.13) (373)
n = 1170 mol
m = nW = (1170mol) (18 g / mol) = 21071g = 21.07 kg
d) The final volume would be found by using BOyles law
P1V1 / T1 = P2V2 / T2
V2 = P1V1 T2 / P2T1
= (300000) (0.71)(373) / (5000000)(473)
= 0.033 m3
e) Now the pressure applied is given as
P = 5000000pa
F = P A =( 5000000) (1.1)(10-4) = 550N
f) The distance the piston cover would be
W = F. d
d = F / W
d = 550 / PV
d = 550 / (5000000)(0.0033)
d = 0.0333 m
The heat transfer would be equal to
Q = m Cv dT
Q =( 21.07kg)(1.996KJ / kg K) ( 100-200)
Q = o.42kJ
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