A piston-cylinder assembly whose piston is resting on top of a set of stops init
ID: 1719023 • Letter: A
Question
A piston-cylinder assembly whose piston is resting on top of a set of stops initially contains 0.1 kg of N_2 with a pressure of 100 kPa and 25 degree C. The volume of the cylinder initially is 0.2 m^3. The gas undergoes a process for which the pressure-volume relationship is pV^1.4 = constant The volume of the final stage is twice the initial condition. There are no significant changes in kinetic or potential energy. Determine the following Final pressure in kPa Final temperature in degree K. Net work done in kJExplanation / Answer
given,
MASS,m=0.1 kg of N2
INITIAL PRESSURE, P1=100kPa
FINAL PRESSURE, P2 =NOT GIVEN
INITIAL TEMPERATURE, T1=25 DEGREE
FINAL TEMPERATURE, T2 =NOT GIVEN
INITIAL VOLUME, V1=0.2 m3
FINAL VOLUME, V2=NOT GIVEN
V1=2V2
Gas undergoes a process from initial state to final state following the relationship PV1.4=Constant, which suggests that the gas undergoes reversible adiabatic process.
To find final pressure ,we can use the relationship PV1.4=CONSTANT which the gas undergoes.
as, P1V11.4=P2V21.4=CONSTANT
putting the values of P1,V1 AND using the relation V1=2V2
We get,
100(0.2)1.4=P2(0.2/2)1.4
Hence, P2=263.9 kPa
therefore the final temperature of the gas is 263.9 kPa
to find the final temperature we can use the following relationship between temperature and volume as the gas undergoes reversible adiabatic process,
T1V11.4-1=T2V21.4-1=CONSTANT
By putting the values of T1,V1 and using V1=2V2,
We get,
25(0.2)1.4-1=T2(0.2/2)1.4-1
Hence T2=50 Degree celcius
Therefore the final temperature of nitrogen gas is 50 Degree celcius
To find the net work done we can use the following relationship of system undergoing reversible adiabatic process
Net work, W=(P1V1-P2V2)/1.4-1
Putting the values of P1,P2,V1,V2 in the above equation ,
we get, W={100(0.2)-263.9(0.1)}/1.4-1
W=-15.957 Joules , here negative sign indicates work is done on the system.
therefore the net work done is 0.015957kJ.
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