A rigid container holds 2.5 mol of an ideal gas at a pressure of 1.2 × 10^5 Pa and a temperature of 320 K. The gas is heated at constant volume until its temperature reaches 480 K. What is the new pressure of the gas?
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Correct answer
A. 1.8 × 10^5 Pa
Principle or equation
For an ideal gas at constant volume, pressure is directly proportional to absolute temperature: P1/T1 = P2/T2.
Why this answer is correct
Using the ideal gas law with constant volume, P/T = constant. Therefore, P2 = P1 × (T2/T1). Substituting P1 = 1.2 × 10^5 Pa, T1 = 320 K, T2 = 480 K, we get P2 = 1.2 × 10^5 × (480/320) = 1.2 × 10^5 × 1.5 = 1.8 × 10^5 Pa.
Example
If a gas at 300 K and 1.0 × 10^5 Pa is heated to 600 K at constant volume, the new pressure is 2.0 × 10^5 Pa.
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