A room at 20oC is heated by a heater of resistance 20 ohm connected to 200 V mains. The temperature is uniform throughout the room and the heat is transmitted through a glass window of area 1 m2 and thickness 0.2 cm. Calculate the temperature outside. Thermal conductivity of glass is 0.2 cal/m Co s and mechanical equivalent of heat is 4.2 J/cal.

If θ is the temperature of outside, heat passing per second through the glass window,dQdt=KAθ1−θ2L=0.2×1×(20−θ)cal0.2×10−2=100(20−θ)And heat produced per second by the heater in the roomP=V2RJs=V2RJcals=200×20020×4.2=476.2 cal sNow as the temperature of the room is constant, the heat produced per second by heater must be equal to the heat conducted through the glass window.100(20−θ)=476.2 ⇒θ=15.24∘C