Question

The pressure of the gas in a constant volume gas thermometer is 70 kPa at the ice point.  Find the pressure at the steam point.

Answer 1

Given:
​Temperature of ice point, T₁ = 273.15 K 
Temperature of steam point, T₂ = 373.15 K
Pressure of the gas in a constant volume thermometer at the ice point, P_1​ = 70 kPa,        
Let P_tr be the pressure at the triple point and P₂ be the pressure at the steam point.
The temperature-pressure relations for ice point and steam point are given below:
For ice point,

\[T_1 = \frac{P_1}{P_{tr}} \times 273 . 16 K\]

\[\Rightarrow 273 . 15 = \frac{70}{P_{tr}} \times {10}^3 \times 273 . 16\]

\[ \Rightarrow P_{tr} = \frac{70 \times 273 . 16 \times {10}^3}{273 . 15} Pa\]

For steam point,

\[T_2 = \frac{P_2 \times 273 . 16}{P_{tr}} K\]

On substituting the value of P_tr ,we get:

\[373 . 15 = \frac{P_2 \times 273 . 15 \times 273 . 16}{70 \times 273 . 16 \times {10}^3} \]

\[ \Rightarrow P_2 = \frac{373 . 15 \times 70 \times {10}^3}{273 . 15}\]

\[ \Rightarrow P_2 = 95 . 626 \times {10}^3 Pa\]

\[ \Rightarrow P_2 \simeq 96 kPa\]

Therefore, the pressure at steam point is 96 kPa.