Three moles of an ideal gas are initially confined in a volume of 50 liters at 2

Question

Three moles of an ideal gas are initially confined in a volume of 50 liters at 20o C. (a) What is the pressure in the gas? The gas is now expanded until its volume is 100 liters and its pressure is only half as much. This is done by either processes ABC or directly from A to C in the diagram. (b) What work is done on the gas for process ABC? (c) How much heat flows into the gas for process ABC? (d) What work is done on the gas in direct process AC? (e) What heat flows into the gas for process AC?

Explanation / Answer

A) Apply, Po*Vo = n*R*To

==> Po = n*R*To/Vo

= 3*8.314*(20+273)/(50*10^-3)

= 1.46*10^5 pa

B) W(ABC) = Po*(V2 - V1)

= 1.46*10^5*(100-50)*10^-3

= 7300 J

C) Apply, P1*V1/T1 = P2*V2/T2

T2 = T1*P2*V2/(P1*V1)

= T1(Po/2 * 2*Vo)/(Po *Vo)

= T1

= 20 + 273

= 293 k

so, there is no temperature change.

so, there is no chnage in internal energy.

heat flown, Q = W(ABC) = 7300 J

D) W(AC) = Po/2*(V2-V1) + 0.5*(V2-V1)*Po/2

= (1.46*10^5/2)*(100-50)*10^-3 + 0.5*(100-50)*10^-3*1.46*10^5/2

= 5475 J

E) heat flown, Q = 5475 J

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