Question

Show that the change in internal energy in a non-isolated system is zero.

Answer 1

Answer:

Internal energy and entropy are both state functions.

Changes in internal energy are directly reflected by the change in temperature during the process. For an isothermal process, there is no change in internal energy.

For an adiabatic process, where, ideally, there is no heat transfer, there is no change in entropy, but a change in internal energy, due to variations in temperature because of compression or expansion.

In a simple refrigeration air conditioning system, most of the evaporation, and some major part of condensarion takes place in liquid-vapour zone. During this process, in the liquid-vapour zone, the temperature remains constant, as the phase change happens. So, there is no change in internal energy, but the entropy varies along with randomness, ie, during condensation (2 to 3) it decreases, while during evaporation(4 to 1), increases. This happens due to heaf transfer in (evaporation) and out (condensation) of the working fluid.

During throttling(3 to 4), part of saturated liquid turns into vapour, leading to increase in entropy.

While during compression(1 to 2), there is no change in entropy, as there is no heat transfer ideally.

If we calculate the changes in internal energy and entropy for the above cycle, they will turn out to be zero.

But, in real life, there is no such thing. Maybe the internal energy changes are very close to zero, once the equipment metal temperatures reach an equilibrium with the process demand, but, because of irreversibilities due to imperfect insulation, friction and flow irreversibilities, change in entropy will always be positive, as the irrevesibilities are heat addition phenomenon.