A brass rod (thermal conductivity 109 J/s m K) has an area of cross section 0.04 m² and length 20 cm. If the two end of the rod are maintained at a temperature difference of 200°C, the rate of heat flow through the rod is ________.

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RRB ALP Fitter 23 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 = 20 cm = 0.2 m, Area, A = 0.04 m2, Temperature difference, ΔT = 200ºC,

Thermal conductivity, k = 109 J/(s m K)

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

\(\frac{Q}{t}=\frac{kAΔ T}{a}\)

\(\frac{Q}{t}=\frac{109\times 0.04\times 200}{0.2}\)

\(\frac{Q}{t}=4360 ~J/s\)

\(\frac{Q}{t}=4.360 ~kJ/s\)