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Near room temperature, how does the internal energy of one mole of a diatomic ideal gas compare to that of one mole of a monatomic ideal gas?A. They have the same internal energy.B. The diatomic gas has 2 times as much internal energy as the monatomic gas.C. The diatomic gas has 2$/ 3$ times as much internal energy as the monatomic gas.D. The diatomic gas has 3$/ 2$ times as much internal energy as the monatomic gas.E. The diatomic gas has 5$/ 3$ times as much internal energy as the monatomic gas.

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Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

Cornell University

University of Washington

Simon Fraser University

Hope College

Lectures

03:15

In physics, the second law of thermodynamics states that the total entropy of an isolated system can only increase over time. The total entropy of a system can never decrease, and the entropy of a system approaches a constant value as the temperature approaches zero.

03:25

The First Law of Thermodynamics is an expression of the principle of conservation of energy. The law states that the change in the internal energy of a closed system is equal to the amount of heat energy added to the system, minus the work done by the system on its surroundings. The total energy of a system can be subdivided and classified in various ways.

02:09

Assume 3 moles of a diatom…

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The temperature of three m…

Two moles of a monatomic i…

Three moles of a monatomic…

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By how much does the tempe…

0:00

Four moles of a monatomic …

05:55

03:19

04:25

One mole of monatomic idea…

02:00

A diatomic gas has a certa…

02:10

One mole of an ideal monoa…

12:22

consider the expansion of …

In lower temperatures, diatomic gas has 5 degrees of freedom, out of which 3 are translational and 2 are rotational. So, according to equipartitian theorem, each degree of freedom contributes to half of n times r times t to the internal energy of the gas. So the internal energy of n moles of diatomic gas will become 5 upon 2 n r t. This is internal energy. For most, if we have only 1 mole of a diatomic guess, so we have internal energy equal to 5 upon 2 r t. This is for 1, more let this is denoted as internal energy for diatomic gas. Let this is named as equation 1 now for monoatomic gases. It has 3 degrees of freedom at all temperatures, so the internal energy of an mos of monatomic gas according to equi partition theorem, is 3 upon 2 n r t. So for 1 mole we have internal energy equal to 3 upon 2 r t. This is inter energy for monatomic gas for 1 mole. Let this name. The equation. 2 now divide equation: 1 by 2, so we get internal energy of diatomic gas upon internal energy of a dial monotonic gas is equal to 5 upon 2 r t whole divide by 3 upon 2 r 3. So from here we get internal energy of diatomic gas. Upon intern energy of monoatomic gas is equal to 5 upon 3 or we can write it as internal energy of a dial diatomic gas is equal to 5 upon 3 times internal of real monoatomic guess. So this relation shows that internal energy of monotonic ardel guess is equal to 5 upon 3 times the internal energy of the manoatomic ideal guess so the statement is correct.

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