Question

An electric heater is used in a room with a total wall area of 137 m² to maintain a temperature of +20°C inside it when the outside temperature is -10°C. The walls have three different layers of materials. The innermost layer is of wood of thickness 2.5 cm, the middle layer is of cement of thickness 1.0 cm and the outermost layer is brick of 25.0 cm. The power of the electric heater will be ______ W. Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of wood, cement, and brick are 0.125, 1.5, and 1.0 watt/m/°C respectively.

Options

• 5000

• 6000

• 9000

• 1000

Answer 1

An electric heater is used in a room with a total wall area of 137 m² to maintain a temperature of +20°C inside it when the outside temperature is -10°C. The walls have three different layers of materials. The innermost layer is of wood of thickness 2.5 cm, the middle layer is of cement of thickness 1.0 cm and the outermost layer is brick of 25.0 cm. The power of the electric heater will be 9000 W. Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of wood, cement, and brick are 0.125, 1.5, and 1.0 watt/m/°C respectively.

Explanation:

K = `(d_1 + d_2 + d_3)/(d_1/K_1 + d_2/K_2 + d_3/K_3)`

The rate of flow of heat is,

`Q/t = KA(theta_1 - theta_2)/((d_1 + d_2 + d_3)`

= 9000 W