The internal energy of a hypothetical substance is given by u(T,v) = 43vT + 7/v, where the units of u are in J/mole, T is in K, and v is in m/mole. Also, for this substance, you have T(dP/dT) = 5P, where the units of P are in Pa. Calculate the Joule coefficient's n at T = 223 K and v = 7.7 m^3/mole.
a. -12.5
b. -18.2
c. -24.0
d. -35.6
e. -29.0