Final answer:
Using the known temperatures and the distance from one end, the temperature gradient is calculated, and this information is used to determine the total length of the bar which is approximately 71.15 cm.
Step-by-step explanation:
To determine the length of the bar where heat flows only along its length and temperatures at different points are known, we can use the concept of linear temperature gradient or rate of change of temperature with length, which is constant in such steady-state conditions. Given that the temperature at the cooler end is 12.4 °C, 0.254 m from the cooler end is 24.9 °C, and the warmer end is 47.4 °C, we can calculate the length of the bar.
First, we determine the temperature gradient using the known temperature and distance:
Temperature gradient = (24.9 °C - 12.4 °C) / 0.254 m = 49.2 °C/m
Next, we use the warmer end temperature to find the total length (let's denote it as L):
(47.4 °C - 12.4 °C) / (Temperature gradient) = L
35 °C / 49.2 °C/m = L
L = 0.7115 m
Thus, the total length of the bar is 0.7115 m or approximately 71.15 cm.
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