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Ch 20: The Micro/Macro Connection
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 20: The Micro/Macro ConnectionProblema 34a
Capitolo 20, Problema 34a

2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy. Which gas has the higher initial temperature?

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Step 1: Recall the formula for the thermal energy of a monatomic ideal gas: \( U = \frac{3}{2} nRT \), where \( U \) is the thermal energy, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in kelvins.
Step 2: Rearrange the formula to solve for temperature \( T \): \( T = \frac{2U}{3nR} \). This equation will allow us to calculate the temperature of each gas based on its thermal energy and number of moles.
Step 3: For gas A, substitute \( U = 5000 \ \text{J} \), \( n = 2.0 \ \text{mol} \), and \( R = 8.314 \ \text{J/(mol·K)} \) into the formula \( T = \frac{2U}{3nR} \). Simplify the expression to find the temperature of gas A.
Step 4: For gas B, substitute \( U = 8000 \ \text{J} \), \( n = 3.0 \ \text{mol} \), and \( R = 8.314 \ \text{J/(mol·K)} \) into the same formula \( T = \frac{2U}{3nR} \). Simplify the expression to find the temperature of gas B.
Step 5: Compare the calculated temperatures of gas A and gas B. The gas with the higher temperature has the higher initial temperature.

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Thermal Energy

Thermal energy refers to the total kinetic energy of the particles in a substance due to their motion. It is directly related to temperature, as higher thermal energy typically indicates higher temperatures. In this context, the thermal energy of each gas is crucial for determining their respective temperatures.
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Volume Thermal Expansion

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. For monatomic gases, this law helps in understanding how the number of moles and thermal energy can influence temperature, allowing us to compare the two gases in the question.
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Ideal Gases and the Ideal Gas Law

Temperature and Molar Heat Capacity

Temperature is a measure of the average kinetic energy of the particles in a substance. For monatomic gases, the molar heat capacity at constant volume (Cv) is a key factor, as it relates the change in thermal energy to the change in temperature. This relationship allows us to calculate and compare the initial temperatures of gases A and B based on their thermal energies and the number of moles.
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Specific Heat & Temperature Changes
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