Question

3 bars of equal length and equal area of cross section are connected in series. Their thermal conductivities are in the ratio 2:4:3 . if the open ends of the first and the last bars are at temperatures 200 degree celcius and 18 degree celcius respectively. calculate the temperature of both the junctions.

Answer 1

The temperature of both the junctions is T1 = 116 °C  and T2 = 74 °C

Explanation:

• Conductivity of the bars are 2x, 4x and 3x length of the bars = L, CSA = A
• Since the bars are connected in series the heat flow through them will be same.

Let ΔH1, ΔH2 and ΔH3 be heat flow in the three bars respectively in time Δt

ΔH1 / Δt = ΔH2 / Δt = ΔH3 / Δt

ΔH1 / Δt = ΔH2 / Δt

• ΔH1 = ΔH2

=> 2xA(T1 – 200)/L = 4xA(T2 – T1)/L

=> 3T1 – 2T2 = 200  ----(1)

• ΔH2 / Δt = ΔH3 / Δt

=> 4xA(T2 – T1)/L = 3xA(18 – T2)/L

=> 4(T2 – T1) = 3(18 – T2)

=> 7T2 – 4T1 = 54   ---2.

Solving equations (1) and (2).

T1 = 116 °C

T2 = 74 °C

Hence the temperature of both the junctions is T1 = 116 °C  and T2 = 74 °C

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Answer 2

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