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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
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Capitolo 18, Problema 2a

Helium gas with a volume of 3.203.20 L, under a pressure of 0.1800.180 atm and at 41.041.0°C, is warmed until both pressure and volume are doubled. What is the final temperature?

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Start by converting the initial temperature from Celsius to Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \). For 41.0°C, calculate the temperature in Kelvin.
Apply the ideal gas law in the form \( PV = nRT \) to relate the initial and final states of the gas. Since the number of moles \( n \) and the gas constant \( R \) remain constant, you can use the combined gas law: \( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \).
Substitute the known values into the combined gas law. The initial pressure \( P_1 = 0.180 \) atm, initial volume \( V_1 = 3.20 \) L, and initial temperature \( T_1 \) in Kelvin. The final pressure \( P_2 = 2 \times 0.180 \) atm and final volume \( V_2 = 2 \times 3.20 \) L.
Rearrange the combined gas law to solve for the final temperature \( T_2 \): \( T_2 = \frac{P_2V_2T_1}{P_1V_1} \).
Substitute the values into the equation and solve for \( T_2 \) to find the final temperature in Kelvin. Remember to check your units to ensure they are consistent throughout the calculation.

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Ideal Gas Law

The Ideal Gas Law, PV=nRT, relates the pressure (P), volume (V), and temperature (T) of a gas with its amount in moles (n) and the gas constant (R). It is crucial for understanding how changes in pressure, volume, and temperature affect a gas. In this problem, it helps determine the final temperature when both pressure and volume are doubled.
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Ideal Gases and the Ideal Gas Law

Temperature Conversion

Temperature conversion is essential when dealing with gas laws, as calculations require temperatures in Kelvin. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature. This conversion is necessary to apply the Ideal Gas Law correctly, ensuring accurate calculations of the final temperature.
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Unit Conversions

Direct and Inverse Proportionality

Understanding direct and inverse proportionality helps analyze how variables in the Ideal Gas Law interact. When pressure and volume are doubled, the relationship between these variables and temperature must be considered. Direct proportionality implies that if pressure and volume increase, temperature must also increase to maintain the equation's balance.
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The Inverse-Square Law for Intensity
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