A piston cylinder contains 1.5 kg water at 200 kPa, 150°C. It is now heated in a process where pressure is linearly related to volume to a state of 600 kPa, 350°C. Find the final volume, the work and the heat transfer in the process.
Answers
Answer:
A spring loaded piston/cylinder contains 1.5 kg of air at 27C and 160 kPa. It is now heated to 900 K in a process where the pressure is linear in volume to a final volume of twice the initial volume. Plot the process in a P-v diagram and find the work and heat transfer.
Take CV as the air.
m₂ m₁ m; m(u₂-₁)=1Q2-1W₂
Process: P= A + BV => 1W₂ IP dV area=0.5(P₁ + P₂)(V₂-V₁)
State 1: Ideal gas.
V₁ mRT₁/P₁ 1.5x 0.287 300/160=0.8072 m³
Table A.7
u₁u(300) 214.36 kJ/kg
State 2: P₂V₂ mRT₂ so ratio it to the initial state properties
P₂V₂/P₁V₁=P₂2/P₁=mRT₂/mRT₁=T₂/T₁ =>
P2 P1 (T2/T1)(1/2)=160 (900/300) (1/2)-240 kPa
Work is done while piston moves at linearly varying pressure, so we get
1W₂=0.5(P₁ + P₂)(V₂ -V₁)=0.5x(160+240) kPa 0.8072 m³= 161.4 kJ Heat transfer is found from energy equation
1Q2 m(u₂-₁)+1W₂=1.5x(674.824-214.36)+161.4-852.1 kJ
Explanation: