Question

At 0 degree celcius the pressure of the gas in constant volume gas thermometer is 30cm Hg. Calculate the temperature when the pressure of the gas is 50 cm of Hg

Answer 1

Answer on Question #67288, Physics / Molecular Physics | Thermodynamics

At 0 degree celcius the pressure of the gas in constant volume gas thermometer is 30cm Hg. Calculate the temperature when the pressure of the gas is 50 cm of Hg

Find: $T_{2} - ?$

Given:

$T_{1} = 273\ \text{K}$

$$P_{1} = \frac{30\ \text{cm Hg}}{76\ \text{cm Hg}} \times 1.013 \times 10^{5}\ \text{Pa} = 0.4 \times 10^{5}\ \text{Pa}$$ $$P_{2} = \frac{50\ \text{cm Hg}}{76\ \text{cm Hg}} \times 1.013 \times 10^{5}\ \text{Pa} = 0.67 \times 10^{5}\ \text{Pa}$$

Solution:

Gay-Lussac's Law:

$$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}} \quad (1)$$ $$\text{Of} \quad (1) \Rightarrow T_{2} = \frac{P_{2}}{P_{1}} T_{1} \quad (2)$$ $$\text{Of} \quad (2) \Rightarrow T_{2} = 457\ \text{K} \quad (3)$$ $$\text{Of} \quad (3) \Rightarrow t_{2} = +184\ {}^{\circ}\text{C}$$

Answer:

$$+184\ {}^{\circ}\text{C} \quad (457\ \text{K})$$

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