A styrofoam sheet of thickness 5 cm and area 0.25 m² has a temperature difference of 40°C between its inner and outer surfaces. The rate of heat flow through the sheet [thermal conductivity is 0.01 J/(s m K)] is:

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RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 3)

Answer 1

Concept:

Conduction:

It is the process by which heat energy is transmitted through collisions between neighboring atoms or molecules.
It occurs more readily in solids and liquids, where the particles are closer together than in gases, where particles are further apart.
The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watts (joules per second).
Formula, rate of heat flow, \(\frac{Q}{t}=\frac{kAΔ T}{a}\),
Where, ΔT = difference in temperature, A = area, k = thermal conductivity, a = thickness of the conductor, Q = heat, t = time

Calculation:

Given,

Thickness, a = 5 cm = 0.05 m, Area, A = 0.25 m², Temperature difference, Δ T = 40ºC, Thermal conductivity, k = 0.01 J/(s m K)

The rate of heat flow through the sheet can be calculated as,

\(\frac{Q}{t}=\frac{kAΔ T}{a}\)

\(\frac{Q}{t}=\frac{0.01\times 0.25\times 40}{0.05}\)

\(\frac{Q}{t}=2.0 ~J/s\)

Hence, the rate of heat flow through the sheet is 2.0 J/s.