Question

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.

Answer #1

a]

During Isothermal process temperature is constant,

P_{1}=Initial pressure

P_{2}=final pressure

V_{1}=Initial Volume

V_{2}=Final volume

T_{1}= T_{2}

P_{1}V_{1}=P_{2}V_{2}

V_{2}= P_{1}V_{1}/P_{2}= (4 ×
10^{7})(1.5)/3 × 10^{7}= 2m^{3}

After Isothermal process,

Gas undergoes isochoric process (Volume will be constant)

P_{2}/T_{2}= P_{3}/T_{3}

T_{3}= P_{3} (T_{2}/P_{2})=
2*10^{7}*400/3 × 10^{7}= 266.67K

After completion of both the process

Final Volume= 2m^{3}

Final temperature= 266.67K

b]

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