The rear window of a car is defrosted by having a transparent film heater attached to the glass. The heater provides a uniform heat flux on the surface that depends on the amount of current passing through it. If the window itself is \(3 \mathrm{~mm}\) thick, the inner surface must be kept at \(15^{\circ} \mathrm{C}\) for defrosting, and the interior and exterior conditions are \(T_{i}=20^{\circ} \mathrm{C}\) \(h_{i}=10 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) and \(T_{o}=-17^{\circ} \mathrm{C}, h_{o}=25 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) :

a. What is the temperature profile through the glass?

b. How much power is required to hold the conditions constant per unit area of glass?

c. If the glass started out at the outside temperature of \(T_{o}\), its density is \(2500 \mathrm{~kg} / \mathrm{m}^{3}\) and heat capacity of \(750 \mathrm{~J} / \mathrm{kgK}\), how much has the glass's internal energy per unit area changed?