	When calculating the internal energy U of the monatomic ideal gas, we use U=3/2 nRT.  Here, n is the number of moles, R is the universal constant, and T is the Kelvin temperature. What is U when considering 2 moles of gas at the temperature of 300 K?  Here, R is a gas constant and it is given as 8.31 J/(mol  K)  

To calculate the internal energy \( U \) of the monatomic ideal gas, we use the formula:

\[
U = \frac{3}{2} nRT
\]

where:
- \( n \) is the number of moles of the gas,
- \( R \) is the universal gas constant, and
- \( T \) is the temperature in Kelvin.

Given:
- \( n = 2 \) moles,
- \( T = 300 \) K,
- \( R = 8.31 \) J/(mol·K).

Now, let's substitute these values into the formula:

\[
U = \frac{3}{2} \times 2 \times 8.31 \times 300
\]

First, calculate the product inside the formula:

\[
U = 3 \times 8.31 \times 300
\]

\[
U = 24.93 \times 300
\]

\[
U = 7479 \text{ J}
\]

So, the internal energy \( U \) is \( \mathbf{7479} \) joules.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the internal energy change if the number of moles was doubled?
2. What happens to the internal energy if the temperature is halved?
3. How does the internal energy of a diatomic gas differ from that of a monatomic gas?
4. How is the internal energy related to the average kinetic energy of the gas molecules?
5. Can the internal energy be negative? Why or why not?

**Tip:** Always remember that the internal energy of an ideal gas depends only on its temperature and the number of moles, not on its pressure or volume.

Learn how to calculate the internal energy U of a monatomic ideal gas using the formula U = (3/2) nRT. Example calculation provided for 2 moles of gas at 300 K with R = 8.31 J/(mol·K).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation