A piston moves upward a distance of 5 cm while 200 J of heat is added (Fig.). Calculate the change in internal energy of the vapour if the spring is originally unstretched.
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Sol . The work needed to raise the weight and compress the spring is
W = (mg)(h) + 
Kx 2 + (P atm ) (h)
= (60) (9.81) (0.05) + 
(50000) (0.5) 2 + (100000) 
(0.05) = 250 J
The first law for a process without kinetic or potential energy changes is
Q – W = Δ U
Thus, we have Δ U = 200 – 250 = – 50 J.
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