Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

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. - Physics

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.

Concept: Measurement of Temperature
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 1 Heat and Temperature
Q 5 | Page 12