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Difficulty: MediumGas Laws and the Ideal Gas Equation

A high-altitude research chamber of fixed volume contains nitrogen gas at an initial pressure of 1.00×105 Pa1.00 \times 10^5\text{ Pa} and a temperature of 27∘C27^\circ\text{C}. The gas is heated until its pressure rises to 2.20×105 Pa2.20 \times 10^5\text{ Pa}. What is the final temperature of the gas in degrees Celsius?

Answer: 387 °C

Answer

387
By Gay-Lussac's Law at constant volume, pressure is directly proportional to absolute temperature. Converting 27∘C27^\circ\text{C} to 300 K300\text{ K}, the final temperature is 300×2.20×1051.00×105=660 K300 \times \frac{2.20 \times 10^5}{1.00 \times 10^5} = 660\text{ K}, which equals 387∘C387^\circ\text{C}.

Step-by-Step Solution

1
Convert initial temperature to Kelvin
T_1 = 300 K
Gas laws require absolute temperature in Kelvin.
2
Apply Pressure Law (P1 / T1 = P2 / T2)
T_2 = 660 K
Since volume is fixed, pressure is directly proportional to absolute temperature.
3
Convert absolute temperature back to Celsius
t_2 = 387 °C
The question asks for the temperature in degrees Celsius.

Key Concept

Pressure Law (Gay-Lussac's Law)
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Topics

Gas Laws and the Ideal Gas Equation

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