Question

A quantity of air is contained in a cylinder provided with a movable piston. Initially the...

A quantity of air is contained in a cylinder provided with a movable piston. Initially the
pressure of the air is 4 × 107 N/m2
, the volume is 1.5 m3
and the temperature is 400 K.
Assume air is an ideal gas. (a) What are the final volume and temperature of the air if it is
allowed to expand isothermally from initial conditions until the pressure is 3 × 107 N/m2
and
then is cooled at constant volume until the pressure is 2 × 107 N/m2
? (b) Draw the P-V
diagram for the processes described above.

Homework Answers

Answer #1

a]

During Isothermal process temperature is constant,

P1=Initial pressure

P2=final pressure

V1=Initial Volume

V2=Final volume

T1= T2

P1V1=P2V2

V2= P1V1/P2= (4 × 107)(1.5)/3 × 107= 2m3

After Isothermal process,

Gas undergoes isochoric process (Volume will be constant)

P2/T2= P3/T3

T3= P3 (T2/P2)= 2*107*400/3 × 107= 266.67K

After completion of both the process

Final Volume= 2m3

Final temperature= 266.67K

b]

On x axis we plot volume and on y axis we plot pressure

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