A square steel bar of side length w = 0.18 m has a thermal conductivity of k = 14.6 J / (s⋅m⋅°C) and is L = 1.7 m long. Once end is placed near a blowtorch so that the temperature is T1 = 88° C while the other end rests on a block of ice so that the temperature is a constant T2. Input an expression for the heat transferred to the cold end of the bar as a function of time, using A-w2 as the cross-s area of the bar.

Question

Joey

Physics

1 April, 19:00

A square steel bar of side length w = 0.18 m has a thermal conductivity of k = 14.6 J / (s⋅m⋅°C) and is L = 1.7 m long. Once end is placed near a blowtorch so that the temperature is T1 = 88° C while the other end rests on a block of ice so that the temperature is a constant T2. Input an expression for the heat transferred to the cold end of the bar as a function of time, using A-w2 as the cross-s area of the bar.

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Solomon Barrett · Answer 1

The conducted heat is of 24.5 W/s

Explanation:

The Fourier's equation for heat conduction is:

q = k * (t1 - t2) * A / l

In this particular case:

q = k * (t1 - t2) * w^2 / l

Replacing:

(I assume the temperature of the ice is 0°C)

q = 14.6 * (88 - 0) * 0.18^2 / 1.7 = 24.5 W/s

The conducted heat is of 24.5 W/s.