The bulb of a mercury thermometer is placed firstin melting ice (at standard pressure), then in steam(at standard pressure), and at last in a liquid X. Thelengths of mercury thread in the uniform tube abovebulb, in the three cases, are 30 mm, 180 mm, and60 mm respectively. What is the temperature of X
Question
The bulb of a mercury thermometer is placed firstin melting ice (at standard pressure), then in steam(at standard pressure), and at last in a liquid X. Thelengths of mercury thread in the uniform tube abovebulb, in the three cases, are 30 mm, 180 mm, and60 mm respectively. What is the temperature of X
Solution
The mercury thermometer is calibrated in such a way that the length of the mercury thread corresponds to the temperature. In this case, we know that the length of the mercury thread is 30 mm in melting ice, which corresponds to a temperature of 0°C, and 180 mm in steam, which corresponds to a temperature of 100°C.
We can use these two points to create a linear equation that relates the length of the mercury thread (L) to the temperature (T). The equation will be in the form of T = aL + b.
First, we can find the slope (a) of the line using the formula a = (T2 - T1) / (L2 - L1), where T1 and T2 are the temperatures and L1 and L2 are the corresponding lengths of the mercury thread. Substituting the given values, we get a = (100 - 0) / (180 - 30) = 100 / 150 = 0.67°C/mm.
Next, we can find the y-intercept (b) of the line using the formula b = T1 - aL1. Substituting the given values, we get b = 0 - 0.67 * 30 = -20°C.
So, the equation that relates the length of the mercury thread to the temperature is T = 0.67L - 20.
Finally, we can find the temperature of the liquid X by substituting the length of the mercury thread in X (60 mm) into the equation. We get T = 0.67 * 60 - 20 = 20°C. So, the temperature of the liquid X is 20°C.
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