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Q. 34

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 567

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Short Answer

mol of monatomic gas initially has of thermal energy. It interacts with mol of monatomic gas , which initially has of thermal energy.
a. Which gas has the higher initial temperature? b. What is the final thermal energy of each gas?

The higher initial temperature is,

The Final Thermal energy of gas is,

See the step by step solution

Step by Step Solution

Step: 1  Find the initial temperature: (part a)

Once we have two systems, each contains thermal energy at a different temperature at the start. When the two systems are coupled, they interact thermally until they attain thermal equilibrium. Each system has its own set of starting thermal energy, which is determined by

Our target is to find the initial temperature of each gas, so we solve equation for to be

For gas ,the number of moles is and the thermal energy is ,so the values in is

For gas ,the number of moles is and the thermal energy is ,so the values in is

As shown by the two results, gas has a higher initial temperature than gas .

.

Step: 2 Thermal energy related to number of moles:

During a thermal interaction, heat is transmitted through collisions between high-energy molecules and low-energy molecules, and both systems eventually reach the same final temperature, which is the equilibrium state. The amount of moles in the form determines the final thermal energy.

.

where is the total initial energy

Step: 3  Final Thermal Energy: (part b)

For gas the number of moles is moles and for the number of moles is moles,the final thermal energy for each gas is

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