Quiescent air is at 20°C (treat air as ideal gas). A plate of depth 50 cm and width 40 cm has a temperature of 40°C on the top surface. Calculate the heat dissipated from the top surface.

The heat dissipated or loss at the top of the surface is given by

Qloss = - KA ∆T

Qloss = - KA (Ts - Ta)

Where

K is thermal conductivity of material

A is the cross-sectional area

L is the thickness or length of material

Ta is the temperature of air.

Ts is the temperature at the surface

Ts-Ta is the difference between skin temperature and air temperature.

Given that,

Temperature of air Ta=20°C

Plate dimensions are 50cm by 40cm

Converting to metre = 0.5m by 0.4m

Area = length * breadth

Area=0.5*0.4

Area=0.2m²

The temperature at surface

Ts=40°C

Let assume an aluminium plate then, k = 0.0263 W/m⋅K,

We don't need to convert the temperature to Kelvin, since we are going to use the change in temp.

Applying the formulas

Qloss = - KA (Ts - Ta)

Qloss = - 0.0263 * 0.2 * (40-20)

Qloss = - 0.0263 * 0.2 * 20

Qloss = - 0.1052J

The heat loss is 0.1052J