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Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 17 - Temperature, Thermal Expansion, and the Ideal Gas LawProblema 43
Capitolo 17, Problema 43

A sealed metal container contains a gas at 30.0°C and absolute pressure 1.00 atm. To what temperature must the gas be heated for the pressure to double to 2.00 atm? (Ignore expansion of the container.)

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Start by identifying the relationship between pressure and temperature for a gas in a sealed container. Since the volume and the amount of gas remain constant, we can use the Gay-Lussac's Law: PT = P1T1, where P is pressure and T is temperature in Kelvin.
Rearrange the formula to solve for the final temperature T2: T2 = P2T1 / P1.
Convert the initial temperature from Celsius to Kelvin, since the gas law requires temperatures in Kelvin. Use the formula: T1 = TC + 273.15. For TC = 30.0, calculate T1.
Substitute the known values into the rearranged formula: T2 = P2T1 / P1, where P1 = 1.00 atm, P2 = 2.00 atm, and T1 is the temperature in Kelvin from the previous step.
After calculating T2 in Kelvin, if needed, convert it back to Celsius using the formula: TC = TK - 273.15. This will give the final temperature in Celsius.

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The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it helps us understand how changes in temperature affect pressure when the volume and amount of gas remain constant.
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