To find the temperature corresponding to a mercury thread length of 4 cm on the thermometer, we can use linear interpolation based on the lengths at the fixed points:
- At 0 degrees Celsius, the length is 1 cm.
- At 100 degrees Celsius, the length is 6 cm.
We can set up a linear relationship between the temperature (T) and the length (L) of the mercury thread.
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Calculate the change in length per degree:
- Length change from 0°C to 100°C: \(6 \text{ cm} - 1 \text{ cm} = 5 \text{ cm}\)
- Temperature change: \(100 \text{°C} - 0 \text{°C} = 100 \text{°C}\)
Length per degree: \[ \text{Length per degree} = \frac{5 \text{ cm}}{100 \text{°C}} = 0.05 \text{ cm/°C} \]
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Establish the equation for length: \[ L = 1 + 0.05T \]
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Set \(L = 4\) cm and solve for \(T\): \[ 4 = 1 + 0.05T \] \[ 4 - 1 = 0.05T \] \[ 3 = 0.05T \] \[ T = \frac{3}{0.05} = 60 \text{°C} \]
So, the temperature corresponding to a mercury thread length of 4 cm is 60 degrees Celsius.