A constant volume air thermometer has a bottle which is partly filled with mercury. Find the ratio of volume of mercury present in the bottle to the volume of the bottle if the volume coefficients of mercury and glass are 1.8 x 10^-4 K^-1 and 6X10^-5 K^-1, respectively.?

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A constant volume air thermometer has a bottle which is partly filled with mercury. Find the ratio of volume of mercury present in the bottle to the volume of the bottle if the volume coefficients of mercury and glass are 1.8 x 10^-4 K^-1 and 6X10^-5 K^-1, respectively.?

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A constant volume air thermometer has a bottle which is partly filled ...

Solution:

Given:
- Volume coefficient of mercury, β_m = 1.8 x 10^-4 K^-1
- Volume coefficient of glass, β_g = 6 x 10^-5 K^-1

To find: The ratio of volume of mercury present in the bottle to the volume of the bottle.

Explanation:
Let V_m be the volume of mercury present in the bottle and V_b be the volume of the bottle.

Since the air thermometer is constant volume thermometer, the volume of the glass bottle remains constant. Therefore, the change in volume is only due to the change in volume of mercury.

Let ΔT be the change in temperature of the thermometer. Then the change in volume of mercury can be calculated as follows:

ΔV_m = V_m β_m ΔT

The change in volume of the bottle can be calculated as follows:

ΔV_b = V_b β_g ΔT

Since the volume of the glass bottle remains constant, the change in volume of the bottle is zero. Therefore,

ΔV_b = 0

V_b β_g ΔT = 0

ΔT = 0

This means that the thermometer is at constant temperature. Therefore, the volume of mercury present in the bottle is equal to the volume of the bottle.

V_m = V_b

The ratio of volume of mercury present in the bottle to the volume of the bottle is:

V_m/V_b = 1

Therefore, the ratio of volume of mercury present in the bottle to the volume of the bottle is 1.

Answer: The ratio of volume of mercury present in the bottle to the volume of the bottle is 1.

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A constant volume air thermometer has a bottle which is partly filled with mercury. Find the ratio of volume of mercury present in the bottle to the volume of the bottle if the volume coefficients of mercury and glass are 1.8 x 10^-4 K^-1 and 6X10^-5 K^-1, respectively.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A constant volume air thermometer has a bottle which is partly filled with mercury. Find the ratio of volume of mercury present in the bottle to the volume of the bottle if the volume coefficients of mercury and glass are 1.8 x 10^-4 K^-1 and 6X10^-5 K^-1, respectively.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A constant volume air thermometer has a bottle which is partly filled with mercury. Find the ratio of volume of mercury present in the bottle to the volume of the bottle if the volume coefficients of mercury and glass are 1.8 x 10^-4 K^-1 and 6X10^-5 K^-1, respectively.?.

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