Question

A constant volume gas thermometer shows pressure readings of 50 cm and 90 cm of mercury at 0 degree Celsius, 100 degree Celsius respectively. What is the temperature of the bath when pressure reading is 60 cm of mercury?

Answer 1

Hint: In this question, we will use the relation between the temperature change and the height change or the mercury reading change. Further, we will get the result by substituting the given values to the expression. Also, we will study some basics of a thermometer and temperature.

Formula used:
$T = \dfrac{{{h_1} - {h_0}}}{{{T_1} - {T_0}}}$

Complete step by step solution:
Thermometers are used to measure temperature. We know that different thermometers are used for different purposes and not all thermometers can measure each quantity because of their limits.
$\eqalign{
  & T = \dfrac{{{h_1} - {h_0}}}{{{T_1} - {T_0}}} \cr
  & \dfrac{{\Delta h}}{{\Delta t}} = \dfrac{{40}}{{100}} \cr} $
Now, we find temperature of the bath for height h=60 cm:
$\dfrac{{{h_1} - {h_0}}}{{{T_1} - {T_0}}} = \dfrac{{\Delta h}}{{\Delta t}} = \dfrac{{40}}{{100}}$
By substituting the given values in the above equation we get:
$ \Rightarrow \dfrac{{60 - 50}}{{T - 0}} = \dfrac{{40}}{{100}}$
$ \Rightarrow \dfrac{{10 \times 10}}{4} = T$
$\therefore T = {25^ \circ }C$
Therefore, we get the required temperature of the bath at the given height and temperature, which is given by the above result.
Additional information: we know that gases are made up of particles that are very far apart. When the temperature is increased the particles of gas move faster and collide more often, resulting in greater resistance of friction. The more is the friction in gases the more is its viscosity.
Furthermore, a thermometer is a device that measures temperature or temperature gradient. A thermometer has two important elements that are:
1. A temperature sensor- bulb of mercury-in-glass thermometer acts as a temperature sensor; in this some changes occur with a change in temperature.
Some means of converting this change into a numerical this change into a numerical value.
2. A clinical thermometer is a small medical thermometer with a short but finely calibrated range. These are used by doctors in clinics. A clinical mercury thermometer has mercury in them which expands with the temperature.

Note: There are different types of thermometer present for different purposes, like- clinical thermometer; laboratory thermometer etc. thermometers have different limits. The S.I unit of temperature is Kelvin (K).