Calculate the change in internal energy of the following system: a 100.0-g bar of gold is heated from 25 ∘C to 50 ∘C during which it absorbs 322 J of heat. Assume the volume of the gold bar remains constant.

The Law states that the change in internal energy (U) of the system is equal to the sum of the heat supplied to the system (q) and the work done ON the system (W)

ΔU = q + W

For the first question, 0.653kJ of heat energy is removed from the system (balloon) while 386J of work is done ON the balloon, thus

ΔU = - 653J + 386J

=-267J

Thus internal energy decrease by 267J

For the second question, 322J of heat energy is added to the system (gold bar) while no work is done on the gold bar, this is an isochoric/isovolumetric process, thus

ΔU = 322J + 0

=322J

Thus internal energy increase by 322J