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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.
Solution
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, P1 = 70 kPa,
Let Ptr 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 Ptr ,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.
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