Question

A volume of air (assumed to be an ideal gas) is first cooled without changing its volume and then expanded without changing its pressure, as shown by the path abc in the figure (Figure 1). Take the graduation p0=2.5×105Pa and the graduation V0=0.05.

Р (Ра) а РоЬ V (m3) о Vo

How does the final temperature of the gas compare with its initial temperature?

How much heat does the air exchange with its surroundings during the process abc?

If the air instead expands from state a to state c by the straight-line path shown, how much heat does it exchange with its surroundings?

Answer 1

How does the final temperature of the gas compare with its initial temperature

apply PV = nRT  

T = PV/nR

Ta = 3Po *Vo /nR

Tc =Po*3Vo /nR = 3Po *Vo /nR

so Ta = Tc

How much heat does the air exchange with its surroundings during the process ABC

Uabc = Uac since internal  energy is a path function

and Ta =Tc so   Uabc = Uac = 0

Wabc = Wab+ Wbc

in  isochoric process Wab = 0

Qabc = Uabc + Wabc = 0 + Wabc = 0 + Wbc

= 2.5*10^5* ( 2* 0.05) =25000 J

the amount of heat exchanged.   25000 J

last part

again we apply the same rule and U = 0, but W equals area under the line ac..

= 1/2*( 2.5*10^5 + 7.5*10^5) *2*0.05 = 50000 J

so Q = 50000 J ( absorbed by the system

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