College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Understanding the Internal Energy of an Ideal Monatomic Gas
Complete the following statement: The internal energy of an ideal monatomic gas is:
1. **independent of the number of moles of the gas.**
2. **proportional to the Kelvin temperature of the gas.**
3. **a constant that is independent of pressure, volume, or temperature.**
4. **dependent on both the pressure and the temperature of the gas.**
5. **proportional to the pressure and inversely proportional to the volume of the gas.**
This question helps to understand the fundamental properties of an ideal monatomic gas in relation to its internal energy. Remember, for an ideal monatomic gas:
- Internal energy ([U]) is directly proportional to the temperature ([T]).
- The relation takes the form [U = (3/2)*n*R*T], where [n] is the number of moles and [R] is the universal gas constant.
### Explanation for Each Option
1. **Independent of the number of moles of the gas:** Internal energy actually depends on the number of moles, as more moles of gas would result in greater internal energy.
2. **Proportional to the Kelvin temperature of the gas:** Correct. The internal energy of an ideal monatomic gas is directly proportional to its temperature. As the temperature increases, the internal energy increases.
3. **A constant that is independent of pressure, volume, or temperature:** Incorrect. Internal energy depends on temperature changes.
4. **Dependent on both the pressure and the temperature of the gas:** Incorrect. For an ideal monatomic gas at constant volume, the internal energy is only a function of temperature.
5. **Proportional to the pressure and inversely proportional to the volume of the gas:** Incorrect. Though pressure and volume are important state functions for gases, internal energy for an ideal gas is not derived from these directly in case of ideal monatomic gases.
This understanding is essential for thermodynamics and statistical mechanics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec99e2ce-f146-4dfd-8358-2828b726596b%2F9c1f44c1-e7fe-4da0-adf0-c1ecae4e3284%2F7n9z5bo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Internal Energy of an Ideal Monatomic Gas
Complete the following statement: The internal energy of an ideal monatomic gas is:
1. **independent of the number of moles of the gas.**
2. **proportional to the Kelvin temperature of the gas.**
3. **a constant that is independent of pressure, volume, or temperature.**
4. **dependent on both the pressure and the temperature of the gas.**
5. **proportional to the pressure and inversely proportional to the volume of the gas.**
This question helps to understand the fundamental properties of an ideal monatomic gas in relation to its internal energy. Remember, for an ideal monatomic gas:
- Internal energy ([U]) is directly proportional to the temperature ([T]).
- The relation takes the form [U = (3/2)*n*R*T], where [n] is the number of moles and [R] is the universal gas constant.
### Explanation for Each Option
1. **Independent of the number of moles of the gas:** Internal energy actually depends on the number of moles, as more moles of gas would result in greater internal energy.
2. **Proportional to the Kelvin temperature of the gas:** Correct. The internal energy of an ideal monatomic gas is directly proportional to its temperature. As the temperature increases, the internal energy increases.
3. **A constant that is independent of pressure, volume, or temperature:** Incorrect. Internal energy depends on temperature changes.
4. **Dependent on both the pressure and the temperature of the gas:** Incorrect. For an ideal monatomic gas at constant volume, the internal energy is only a function of temperature.
5. **Proportional to the pressure and inversely proportional to the volume of the gas:** Incorrect. Though pressure and volume are important state functions for gases, internal energy for an ideal gas is not derived from these directly in case of ideal monatomic gases.
This understanding is essential for thermodynamics and statistical mechanics.
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