2. A piston-cylinder assembly contains 1 kg of nitrogen at 200 kPa with an initi
ID: 703923 • Letter: 2
Question
2. A piston-cylinder assembly contains 1 kg of nitrogen at 200 kPa with an initial volume of 0.5 m3. Heat transfer causes the nitrogen to expand slowly at a constant temperature. The final volume is twice the initial volume. Determine the magnitude of the heat transfer required. 3. Two streams of water enter an adiabatic mixing chamber. The first stream enters at a rate of 50 lb/s at 50 psia and 400 F. The second stream enters at a rate of 150 lb/s at 50 psia and 70 F. The exit pressure is 50 psia. Determine the exit mass flow rate in lb/s, temperature in °E, and enthalpy in Btu/lbm.Explanation / Answer
2.
Given:
mass of nitrogen = 1kg
molar mass of nitrogen =28kg/kmol
P=200kPa
initial volume = 0.5 m3
temp is constant in this process
final volume is twice of initial
therefore final Volume =1 m3
using PV = nRT we can estimate Temp . of process
200*0.5=(1/28)*8.314*T
T=336.78K
to determine the heat transfer required
this is a isothermal process
so
Q= -W=RTln(V2/V1)=8.314*336.78ln(1/0.5) =1940.804 kJ/kmol
so as there are 1/28 kmol of nitrogen in cylinder
heat transfer required = (1/28)*1940.804 =69.3144kJ
3.
pressure is constant in this process
mass balance
m1+m2 = m out
50 lb/s+150 lb/s = m out
exit mass flowrate =200 lb/s.
temp. in F
by first law of thermodynamics
m1h1 +m2h2 =(m1+m2)h3
as h =h(T)
m1T1+m2T2 =(m1+m2)T3
50*400+150*70 =200*T3
T3=152.5oF
ethalpy in Btu/lb
enthalpy =280.48189146608kJ/kg
=265.845 Btu/kg
=120.58 Btu/lbm
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