Question

An ideal gas with ?=1.4 occupies 3.0L at 300 Kand 100kPa pressure and is compressed adiabatically until its volume is 2.0 L. It's then cooled at constant pressure until it reaches 300 K, then allowed to expand isothermally back to stateA.

Find the net work done on the gas and Vmin?

Answer 1

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An ideal gas with \(\gamma=1.4\) occupies 4.5 L at 300 K and 120 kPa pressure and is compressed adiabatically until its volume is 2.0L . It's then cooled at constant pressure until it reaches 300 K, then allowed to expand isothermally back to state A.

Find the net work done on the gas.

Find the minimum volume reached.

n=PV/rT =120*4.5/(8.31*300) =0.217

first compressed adiabatically
(P2/P1) =(V1/V2)^?

hence P2 =(120)(4.5/2)^1.4 =373.45 kPa

T2 =T1*P2*V2/P1V1 =414.95 K

T3/T2 =V3/V2 ....presure constant

hence V3 =1.446 L

hence minimum volume reached is 1.446 L

work done = nrTlnVa/Vb+ P2(V3-V2)-nr(T2-T1)/(? -1)

=0.217*8.31*300ln(4.5/1.446) + 373.45(1.446-2) -0.217(414.95-300)/(1.4-1)

= -344.9 J