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i dont even know where to begin on this one. Can somebody show me steps to help me out please?
The ends of a thin bar are maintained at different temperatures. The temperature of the cooler end is 12° C, while the temperature at a point 0.14 m from the cooler end is 23° C and the temperature of the warmer end is 45° C. Assuming that heat flows only along the length of the bar (the sides are insulated), find the length of the bar.
1 Answer
- Steve4PhysicsLv 76 years ago
The bar is in a steady-state with no heat-loss through the sides. This means the temperature changes *linearly* along the length of the bar. Look at the graph in the link - it's a straight line.
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Point A is the cooler end (at temperature 12°C).
Point B is 0.14m from the cooler end (at temperature 23°C).
Point C is the hotter end (at temperature 45°C).
Draw a diagram showing the above data and sketch the graph to help you understand what is happening.
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You now need some basic maths. Here's one method.
From A to B the temperature change = 23°C - 12°C = 11°C
The distance AB = 0.14m
From A to C the temperature change = 45°C - 12°C = 33°C
We want distance AC
By proportion (because graph is straight):
AC/AB = 33°C/11°C = 3
AC = AB x 3 = 0.14x 3 = 0.42m
