A thermometer has a mercury thread of length 18 mm at 0°C and 138 mm at 100°C. What is the temperature of the…

Question

A thermometer has a mercury thread of length 18 mm at 0°C and 138 mm at 100°C. What is the temperature of the liquid if the mercury thread is 118 mm long?

ScanSolve AI Tutor · Accepted Answer

To calculate the temperature of the liquid using an uncalibrated thermometer, we use the linear relationship between the length of the mercury thread and the temperature.

Identify the given values.
Length at melting ice ( $0^\circ C$ ), $L_0 = 18\, \text{mm}$
Length at steam ( $100^\circ C$ ), $L_{100} = 138\, \text{mm}$
Length at unknown temperature ( $T$ ), $L_T = 118\, \text{mm}$
Apply the formula for temperature conversion.
The temperature $T$ can be calculated using the formula:
$T = \frac{L_T - L_0}{L_{100} - L_0} \times 100^\circ C$
Substitute the values into the formula and calculate.
$T = \frac{118\, \text{mm} - 18\, \text{mm}}{138\, \text{mm} - 18\, \text{mm}} \times 100^\circ C$ $T = \frac{100\, \text{mm}}{120\, \text{mm}} \times 100^\circ C$ $T = \frac{10}{12} \times 100^\circ C$ $T = \frac{5}{6} \times 100^\circ C$ $T = \frac{500}{6}^\circ C$ $T = \frac{250}{3}^\circ C$ $T \approx 83.33^\circ C$
The temperature of the liquid is $83.33^\circ C$ .

A thermometer has a mercury thread of length 18 mm at 0°C and 138 mm at 100°C. What is the temperature of the liquid if the mercury thread is 118 mm long?

Answer

Step-by-step solution

Identify the given values.

Apply the formula for temperature conversion.

Substitute the values into the formula and calculate.

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