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The boiling point of mercury is ${367^0}\,C$ . A mercury thermometer can be used to measure a temperature of ${500^0}\,C$ ;
A. By filling the space above mercury with oxygen at high pressure
B. By filling the space above mercury with nitrogen at low pressure
C. By filling the space above mercury with nitrogen at high pressure
D. By keeping the space above mercury as vacuum

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Answer
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Hint: The boiling point of a substance is the temperature at which the pressure of the substance becomes equal to the atmospheric pressure. If the pressure increases then the boiling point for the same fluid will increase. And if the pressure is decreased then the fluid will boil at lower temperatures.

Complete answer:
The temperature in the surrounding increases as the mercury expands and hence the gas filled in the thermometer compresses and it applies more pressure on the mercury thereby increasing the boiling point. If the gas reacts with mercury then it may give incorrect readings.

Let’s check each option.
In this case oxygen is used at high pressure. As the oxygen is at high pressure therefore it can be used to increase the readings of mercury. But oxygen at higher pressure reacts with mercury. Therefore, it may result in incorrect readings. As a result, we cannot use oxygen. Therefore, option A is an incorrect option.

In this case, nitrogen is used at low pressure. At low pressure, nitrogen will lower the boiling point instead of increasing it. Hence, it cannot be used to measure higher readings.Option B is also incorrect.

Filling nitrogen at high pressure will be helpful. Being at high pressure, it will increase the boiling point and hence provide a greater range of readings. Also, nitrogen does not react with mercury at higher temperature.Therefore, option C is the correct answer.

If the space above mercury is kept vacant, this will reduce the pressure and hence boiling point will also decrease. This leads to lesser range in readings. Therefore, option D is also incorrect.

Hence, option C is the correct answer.

Note: Remember that boiling point of a substance is the temperature at which its pressure is equal to the atmospheric pressure. At higher altitudes, the pressure is lower, as a result, water boils at lower temperature. By increasing the pressure, we can increase the boiling point.