Question & Answer: Consider a system that consists of 1 mole of idel gas and is taken through the cycle shown…..

Consider a system that consists of 1 mole of idel gas and is taken through the cycle shown below from (1–>2–>3). Please complete and explain a) and b) as simply as possible. Thank you.

Consider a system that consists of 1 mole of ideal gas and is taken through the cycle shown below from (1→293). (a) Determine the temperatures at points 1, 2, and 3. 1.0 isotherm 0.5 22.4 44.8 V (dm) (b) Calculate w for each step (192 and 2→3)

Expert Answer

Answer

Temperature at one and three are same since it is a isotherm

So applying PV=N*R*T

P=pressure,v=volume,N=Number of moles,R=gas constant ,T=temperature

P=1atm=1.0135*10^5pa

V=22.4*10^-3 m3

N=1

R=8.314J/mol-k

So on substituting

1.0135*10^5*22.4*10^-3 =1*8.314*T

T=273K(at 1 and 3)

At point 2

Applying P*V=n*R*T

P=1*1.0135*10^5 pa

V=44.8*10^-3 m3

N= 1 mole

R=8.314 J/mol-k

So on substituting we get

T=546k

For 2nd part

Work done in 1—2 is

P(V2-V1)

Since it is a constant pressure process here V2= final volume

V1=initial volume

So work done is 1*1.0135*10^5(44.8-22.4)*10^-3

So work done is 2238.4 J

For 2nd step 2—–3 work done is zero since it is constant volume process

1*1.0135*10^5*44.8*10^-3 =1*8.314

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