Q. 12

# A cubical box of volume 216 cm^{3} is made up to 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is 5°C in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.

Answer :

**Given:**Volume of the box : V = 216 cm

^{3}= 216× 10

^{-6}m

^{3}.

Thickness of the box: x = 0.1 cm = 0.001 m

Power of the heater : P = 100 W

Temperature difference : ΔT = 5 °C

**Formula used:**

Rate of amount of heat flowing or heat current is given as:

Here, Δθ is the amount of heat transferred, ΔT is the temperature difference, K is the thermal conductivity of the material, A is the area of cross section of the material and x is the thickness or length of the material.

Volume of the cube is a

^{3}. Where a is the side of the cube.

∴ a = (216× 10

^{-6})

^{1/3}= 0.06 m

As heat will be transferred from all the sides of the cube,

Surface area of the cube is : A = 6a

^{2}

∴ A = 6× (0.06)

^{2}= 0.0216 m

^{2}.

We know that,

Power = Energy per unit time

Thus,

Substituting we get,

Rate this question :

Assume that the total surface area of a human body is 1.6 m^{2} and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is 37°C. Stefan constant σ is 6.0 × 10^{−8} W m^{−2} K^{−4}.

Calculate the amount of heat radiated per second by a body of surface area 12 cm^{2} kept in thermal equilibrium in a room at temperature 20°C. The emissivity of the surface = 0.80 and σ = 6.0 × 10^{−8} W m^{−2} K^{−4}.

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length cross-sectional area and thermal conductivity of each rod are ℓ, A and K respectively. The ends A, E and F are maintained at temperatures T_{1}, T_{2} and T_{3} respectively. Assuming no loss of heat to the atmosphere, final the temperature at B.

HC Verma - Concepts of Physics Part 2

Find the rate of heat flow through a cross-section of the rod shown in figure (θ_{2}> θ_{1}). Thermal conductivity of the material of the rod is K.

HC Verma - Concepts of Physics Part 2