neon, a monatomic gas, that starts out at conditions of standard temperature and pressure (273.15 K, 105 Pa). Alice heats the gas at constant volume until its pressure is doubled, then Bob further heats the gas at constant pressure until its volume is doubled. If Alice and Bob assume that neon behaves as an ideal gas, then how much heat have they added to the gas for the entire process.

819.45 K

Explanation:

Use the Ideal Gas Law to make sense of this problem, PV = nRT. From this equation, we know that pressure is directly proportional to temperature and that volume is also directly proportional to temperature. Therefore, doubling the temperature would double the pressure, and doubling the temperature would also double the volume. In the described scenario, the temperature is doubled twice, so the temperature is quadrupled (i.e. three times its original amount has been added).

The initial temperature was 273.15 K. Multiply this by 3 to get your answer of 819.45 K.

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