The figure ( Figure 1 ) shows a thermodynamic process followed by 120mg of heliu

Question

The figure (Figure 1) shows a thermodynamic process followed by 120mg of helium.

Part A) Determine the pressure (in atm) of the gas at points 1, 2, and 3.

Part B) Determine the temperature (in °C) of the gas at points 1, 2, and 3.

Part C) Determine the volume (in cm^3) of the gas at points 1, 2, and 3.

Part D) How much work is done on the gas during each of the three segments? (in Joules)

Part E) How much heat energy is transferred to or from the gas during each of the three segments? (in Joules)

Explanation / Answer

number of moles of helium =0.120/4=0.03moles

So at 1

Pressure p1=nRT/V =0.03*82.05*406/1000 atm (Here R=82.05cm3 atm K−1 mol−1

=.999 atm

==1atm

So pressure at p2 is 5p1 = 5 atm

And pressure at 3 is p3=p1=1atm

given T1=406 K

Process 1->2 is isochoric i.e no change in volume

So

p1/p2 =T1/T2

=>T2=5T1=2030K

Since 2->3 is an isothermal process

T3=T2=2030K

Given Volume V1=1000cm^3

So V2= 1000cm^3 (no change in volume)

Now 2->3 is iso thermal process so

P2 V2 =P3 V3

=>V3=5V2=5000cm^3

Work done in process 1->2 is 0(No change in volume)

process 2->3 is nRTln(P2/P3) =.03*8.21*2030*ln(5/1)=803.88 J

process 3->1 is p(V1-v3) = 1*(1000-5000)*0.101J=-404J

So total work done is 399J

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