A thermopane window consists of two sheets of glass separated by a volume filled with air (which we will model as N₂, where κ = 0.0240 J K^-1 m^-1 s^-1). For a thermopane window that is 1 m² in area with a separation between glass sheets of 3 cm, what is the loss of energy when:

a. the exterior of the window is at a temperature of 10°C and the interior of the window is at a temperature of 22°C?

b. the exterior of the window is at a temperature of −20°C and the interior of the window is at a temperature of 22°C?

c. the same temperature differential as in part (b) is used but the window is filled with Ar (κ = 0.0163 J K^–1 m^–1 s^–1) rather than N₂?