A metal bar is used to conduct heat. When the temperature at one end is 100°C and at the other is 20°C, heat is transferred at a rate of 32 J/s. The bar is then stretched uniformly to twice its original length. If again it has ends at 100°C and 20°C, at what rate will heat be transferred between it ends?Select one:a.4 J/sb.32 J/sc.8 J/sd.16 J/s
Question
A metal bar is used to conduct heat. When the temperature at one end is 100°C and at the other is 20°C, heat is transferred at a rate of 32 J/s. The bar is then stretched uniformly to twice its original length. If again it has ends at 100°C and 20°C, at what rate will heat be transferred between it ends?Select one:a.4 J/sb.32 J/sc.8 J/sd.16 J/s
Solution
The rate of heat transfer in a metal bar is given by the equation Q/t = kA(T1-T2)/L, where:
Q/t is the rate of heat transfer, k is the thermal conductivity of the material, A is the cross-sectional area, T1 and T2 are the temperatures at the two ends, and L is the length of the bar.
In this case, when the bar is stretched to twice its original length, the cross-sectional area A will be halved (since the volume remains constant). Therefore, the new rate of heat transfer will be half the original rate.
So, if the original rate was 32 J/s, the new rate will be 32/2 = 16 J/s.
So, the answer is d. 16 J/s.
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