Question

# An ideal gas with γ=1.4 occupies 5.0 L at 300 K and 120 kPa pressure and...

An ideal gas with γ=1.4 occupies 5.0 L at 300 K and 120 kPa pressure and is heated at constant volume until its pressure has doubled. It's then compressed adiabatically until its volume is one-fourth its original value, then cooled at constant volume to 300 K , and finally allowed to expand isothermally to its original state.

Find the net work done on the gas. W= ___J

Constant volume process:(1-2)

P1/P2 = T1/T2

120/240 = 300/T2

T2= 600 k

Work done during constant volume process is zero.

PV = constant.

P2V2 = P3V3

P3= P2(V2/V3)

= 240(5/1.25)1.4 = 1671.46 kpa

From ideal gas equation, we will find T3.

P2/P3 = T2/T3.

240/1671.46= 600/T3

T3 = 4177.65 k.

Work done during this process can be given as:

W2-3 = P2V2[(1/-1){(V2/V3)-1 -1}]

By putting values we get:

W2-3= 2223.30 J

Constant volume process(3-4):

Work done will be zero

Constant temperature process(4-1):

Work done can be given as:

W4-1 = -P1V1ln(V1/V4)

= 120kpa×0.005×ln(5L/1.25L)

= -831.78 J

Total work done on gas will be:

W = 2223.30-831.78 =1391.52 J

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