The first law of thermodynamics can be written as dU = dQ - pdV. If we rearrange this and write dQ = dU + pdV, then this seems to imply that a function Q = Q(U,V) exists, which we already know is not true. Which of the following statements is wrong? (You can check some of these statements for an ideal gas.)
- Although dQ is not an exact differential, dQ/T is exact, so T is an integrating factor for the heat.
- The mixed second partial derivatives of Q(U,V) are equal.
- The mixed second partial derivatives of s(U,V) are equal, but those of Q(U,V) are not.
- Dividing dQ by T produces dQ/T = (1/T)dU + (p/T)dV, which does have equal mixed second partial derivatives.