Question

A gas expands when 606 j of energy is added to it as heat. the expanding gas does 418 j of work on its surroundings.

a. what is the overall change in the internal energy of the gas?
b. if the work done by the gas were equal to 1212 j (rather than 418 j)

Answer 1

a) Heat added Q=606 J
Work W = 418 J
From first law of thermodynamics,
Change in internal energy [ Uf - Ui ] = Q - W
Change in internal energy [ Uf - Ui ]=606 -418=188 J

Change in internal energy [ Uf - Ui ]= 188 J
b ) work W2 = 1212 J
heat exchanged Q2 = ?
Initial energy of this process Ui2=Uf of previous=Ui +188


Final energy Uf2=initial energy of previous process=Ui
Change in internal energy of second process= [ Uf2 - Ui2 ]

Change in internal energy of second process=Ui-(Ui+188)
Change in internal energy of second process= -188 J
Q2=W2+(Uf2 -Uf1)

Q2 =1212 -188=1024 J

Answer 2

a)
Q=606 J
W = 418 J
From first law of thermodynamics,
[ Uf - Ui ] = Q - W
[ Uf - Ui ]=606 -418=188 J
[ Uf - Ui ]= 188 J

b )
W2 = 1212 J
Q2 = ?
Ui2=Uf =Ui +188
Uf2=Ui
[ Uf2 - Ui2 ]=Ui-(Ui+188)
-188 J
Q2=W2+(Uf2 -Uf1)
Q2 =1212 -188=1024 J
Q added in second step (b) so that internal energy is equal to initial internal energy of step (a)=1024 J