For an ideal gas in a sealed container, if you double the pressure and double the volume, while keeping everything else the same, what has happened to the temperature?

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To analyze this, recall the ideal gas law: PV = nRT, where n and R are constants for a given amount of gas and universal constant, respectively.

Option 1: The temperature is now double its original value. If T were doubled, then RT would double, meaning PV would have to double as well. However, we have P increased by a factor of 2 and V increased by a factor of 2, so PV increases by a factor of 4, not 2. So this option misstates the consequence for T.

Option 2: The temperature is now half its original value. Halving T would cut RT in half, requiring PV to be halved. But PV actually becomes four times larger (2P × 2V = 4PV), so this cannot be correct.

Option 3: The temperature is now four times its original value. Since PV increases by a factor of 4 while nR stays the same, RT must increase by the same factor to keep PV = nRT. Therefore T must be quadrupled to satisfy the equation, making this option consistent with the ideal gas law.

Option 4: The temperature is one-quarter of its original value. Reducing T to a quarter would reduce RT by a factor of 4, which would require PV to drop by the same factor, contradicting the given that P and V each doubled (PV increased by 4).

Option 5: The temperature is equal to its original value. Equality would imply RT is unchanged, so PV would remain unchanged, which conflicts with the stated doubling of pressure and volume. This option ignores the change in PV and is therefore incorrect.

In summary, only when T increases to four times its original value does the relationship PV = nRT hold under the given changes (P → 2P, V → 2V) with n constant. The other options fail to align with PV scaling dictated by the ideal gas law.

PHYS 2305 Spring 25 Lin Quiz 11 - Chapter 18 (18.1-18.3, 18.5-18.7)

For an ideal gas in a sealed container, if you double the pressure and double the volume, while keeping everything else the same, what has happened to the temperature?

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