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Answer :
Final answer:
Pressure in a constant volume gas thermometer changes linearly with temperature. Therefore, by knowing two pairs of pressure and temperature values, one can derive a direct linear relationship and find the temperature corresponding to any pressure.
Explanation:
The question revolves around the concepts of gas laws that describe how the pressure of a gas tends to change with temperature. In this case, we have a constant volume gas thermometer, which means the volume within the thermometer does not change, only the pressure does, as the temperature changes.
Using the two known data points (0ºC and 100ºC corresponding to 28.6cm and 36.6cm of mercury respectively), we can derive the method to calculate the temperature corresponding to any pressure. It's assumed that the pressure-temperature relationship is linear, as is normally the case at standard conditions.
For this, we would use an equation of linear variation: P = P0 + kT where P and T are the pressure and temperature respectively. To find the constant 'k', you can determine it from the two given pairs of (T, P) values (0ºC, 28.6cm) and (100ºC, 36.6cm). Then, you can put the value of 'k' and P (which is 35.0cm here) in the equation to determine the corresponding T value.
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