A well-lagged thin metal rod of length 0.2 m has a temperature gradient of 416 K m\(^{-1}\). If one end is at 233º C, what is the temperature at the other end?
Answer: D
Given a rod of length \( L = 0.2 \, \text{m} \) with a temperature gradient of \( 416 \, \text{K/m} \) and one end at \( T_1 = 233^\circ \text{C} \):
\(\Delta T = \text{gradient} \times L = 416 \, \text{K/m} \times 0.2 \, \text{m} = 83.2 \, \text{K}\)
The temperature at the other end \( T_2 \) is:
\(T_2 = T_1 + \Delta T = 233^\circ \text{C} + 83.2 \, \text{C} = 316.2^\circ \text{C}\)
Thus, the temperature at the other end is \( 316.2^\circ \text{C}\).
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