Consider two reservoirs at unknown temperatures. The entropy of reservoir 1 is defined by the function \(S_{1}=a E^{2}\), where \(a=1.00 \mathrm{~J}^{-2}\), and that of reservoir 2 is defined by the function \(S_{2}=b E e^{-c E}\), where \(b=3.00 \mathrm{~J}^{-1}\) and \(c=\) \(1.00 \mathrm{~J}^{-1}\).

(a) What is the entropy gradient of \(S_{1}\) when \(E=1.00 \mathrm{MJ}\) ?

(b) What is the entropy gradient of \(S_{2}\) for all values of \(E\) ?

(c) What is the entropy gradient of \(S_{2}\) for \(E=1.00 \mathrm{~J}\) ?