Change in heat for isothermal processes and internal energy in cyclic processes

[ice87]

What is the equation to find the change in heat of a system that is isothermal?

And also, for a PV graph, if the state of the system loops back onto itself, as in it starts at a and ends at a, is the total change in internal energy always 0?

 

[Andrew Mason]

What is the equation to find the change in heat of a system that is isothermal?

Since PV=nRT, if T does not change, PV is constant. So the internal energy of the system does not change. As a result, there has to be heat flow to or from the system when work is done by or to the system (if it is compressed, heat is lost to the system; if it expands isothermally, it absorbs heat). The heat flow is: $\Delta Q = \Delta U + P\Delta V = P\Delta V$.

And also, for a PV graph, if the state of the system loops back onto itself, as in it starts at a and ends at a, is the total change in internal energy always 0?

Yes. If PV is the same, T is the same (PV=nRT). Since $U = nC_vT$, if the temperature is the same and n does not change, internal energy is the same.

AM