QuestionJune 27, 2025

2. Solving for Temperature A gas at constant volume has a pressure of 5.0 atm at a temperature of 400 K. What is the temperature when the pressure increases to 7.5 atm?

2. Solving for Temperature A gas at constant volume has a pressure of 5.0 atm at a temperature of 400 K. What is the temperature when the pressure increases to 7.5 atm?
2. Solving for Temperature
A gas at constant volume has a pressure of 5.0 atm
at a temperature of 400 K. What is the temperature
when the pressure increases to 7.5 atm?

Solution
4.5(212 votes)

Answer

T_2 = 600 K Explanation 1. Use Gay-Lussac's Law Gay-Lussac's Law states that for a gas at constant volume, the pressure is directly proportional to its temperature: \frac{P_1}{T_1} = \frac{P_2}{T_2}. 2. Substitute Known Values Given P_1 = 5.0 atm, T_1 = 400 K, and P_2 = 7.5 atm. Substitute these into the formula: \frac{5.0}{400} = \frac{7.5}{T_2}. 3. Solve for T_2 Rearrange to find T_2: T_2 = \frac{7.5 \times 400}{5.0}.

Explanation

1. Use Gay-Lussac's Law<br /> Gay-Lussac's Law states that for a gas at constant volume, the pressure is directly proportional to its temperature: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$.<br />2. Substitute Known Values<br /> Given $P_1 = 5.0$ atm, $T_1 = 400$ K, and $P_2 = 7.5$ atm. Substitute these into the formula: $\frac{5.0}{400} = \frac{7.5}{T_2}$.<br />3. Solve for $T_2$<br /> Rearrange to find $T_2$: $T_2 = \frac{7.5 \times 400}{5.0}$.
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