Question

2. A vessel with a piston cylinder attached to a spring (see Figure 1) contains CO2 with a volume of 500 L, a pressure of 200 kPa and a temperature of 25degree C (State 1). heat is transferred to the vessel and it starts to expand until the piston just touches the stops. The pressure at this state is 400 kPa and the temperature is 500 degree C (State 2). More heat is added to the vessel until the pressure is equal to 600 kPa (State 3). Data for CO2: R = 0.1889 kJ/kg.K, Cv = 0.657 kJ/kg.K and Cp = 0.845 kJ/kg.K Treating CO2 as an ideal gas, answer the following: a) Calculate the mass of CO2 (in kg). b) Calculate the volume at State 2 (in m^3). c) Calculate the temperature in State 3 (in degree C). d) Calculate the total boundary work from State 1 to State 3 (in kJ). e) Calculate the amount of heat Q12 and Q23 (in kJ).

Answer 1

state 1

$V_{1}=500L$

$P_{1}=200kPa$

$T_{1}=25^{\circ}C=298 K$

$R=8.314 LkPaK^{-1}mol^{-1}$

using ideal gass equation

$PV=nRT$

$n=\frac{PV}{RT}$

$\Rightarrow n=40.362 mol$

mass of CO₂ per mole is 44 gram

$total mass=n*44 gram$

$total mass=1775.928 gram$

$total mass=1.776 Kg$

state 2

$V_{2}=let x L$

$P_{2}=400kPa$

$T_{1}=500^{\circ}C=773 K$

$R=8.314 LkPaK^{-1}mol^{-1}$

using ideal gass equation

$PV=nRT$

$V=\frac{nRT}{P}$

$V_{2}=648.49L=0.648 m^{3}$

state 3

$V_{3}=648.49L$

$P_{3}=600kPa$

$T_{1}=let x K$

$R=8.314 LkPaK^{-1}mol^{-1}$

using ideal gass equation

$PV=nRT$

$T=\frac{PV}{nR}$

$T_{3}=1159.5K=886.5^{\circ}C$

taking expternal pressure equal to 1 Atm=101.32kPa

boundry work

$W=-P_{ext}\Delta V$

$W=-P_{ext}(V_{3}-V_{1})$

$W=-15045 kPaL=-15.045kJ$

$Q_{23}=mC_{p}(T_{3}-T_{2})$

$Q_{23}=170.33KJ$

now change in internal energi from 1-2

$\Delta U=mC_{v}(T_{3}-T_{1})$

$\Delta U=686.68KJ$

$Q_{total}=\Delta U+W$

$Q_{total}=\Delta U+W$

$Q_{total}=(686.68-15.045)KJ$

$Q_{total}=671.63KJ$

$Q_{total}=Q_{12}+Q_{23}$

$Q_{12}=Q_{total}-Q_{23}$

$Q_{12}=501.30KJ$