Find the internal energy of 2.0 mol of argon at 273 K and 1.0 atm. If the gas pressure and vol

Name: Problem 33, Chapter 14: Essential College Physics
Uploaded: 2021-06-03T14:43:03-08:00
Duration: 2 min 56 s
Channel: Ajay Singhal
Description: Find the internal energy of 2.0 mol of argon at 273 K and 1.0 atm. If the gas pressure and volume both double, what's the change in internal energy?

step 1 belongs to the laws of thermodynamics in which we have to determine the internal energy u of a m

Question

Find the internal energy of $2.0 \mathrm{~mol}$ of argon at $273 \mathrm{~K}$ and 1.0 atm. If the gas pressure and volume both double, what's the change in internal energy?

   Find the internal energy of $2.0 \mathrm{~mol}$ of argon at $273 \mathrm{~K}$ and 1.0 atm. If the gas pressure and volume both double, what's the change in internal energy?

Essential College Physics

Andrew F. Rex,… 1st Edition

Chapter 14, Problem 33

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Solved by Expert Ajay Singhal

06/03/2021

Step 1

The formula for internal energy (U) of an ideal gas is given by: \[ U = \frac{3}{2} nRT \] where n is the number of moles, R is the gas constant, and T is the temperature. Substituting the given values, we get: \[ U = \frac{3}{2} \times 2.0 \, \text{mol} \times Show more…

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Find the internal energy of $2.0 \mathrm{~mol}$ of argon at $273 \mathrm{~K}$ and 1.0 atm. If the gas pressure and volume both double, what's the change in internal energy?

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Key Concepts

Internal Energy of an Ideal Gas

The internal energy of an ideal gas is determined solely by its temperature and the degrees of freedom of its molecules. For a monatomic gas such as argon, the internal energy is given by U = (3/2)nRT, where n is the number of moles and R is the universal gas constant. This formula reflects that the energy is attributed to the kinetic energy of the atoms.

Temperature Dependence of Internal Energy

In an ideal gas, the internal energy is independent of the gas’s pressure and volume. Since U depends only on temperature, any changes in pressure and volume that do not alter the temperature will result in no change in the internal energy. This principle is a direct consequence of the definition of ideal gases and the state function property of internal energy.

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