Two moles of a monatomic ideal gas such as helium is compressed adiabatically and reversibly from a state (4.5 atm, 6.5 L) to a state with pressure 5 atm. For a monoatomic gas y = 5/3. (a) Find the volume of the gas after compression. final (b) Find the work done by the gas in the process. W= L.atm (C) Find the change in internal energy of the gas in the process.
Two moles of a monatomic ideal gas such as helium is compressed adiabatically and reversibly from a state (4.5 atm, 6.5 L) to a state with pressure 5 atm. For a monoatomic gas y = 5/3. (a) Find the volume of the gas after compression. final (b) Find the work done by the gas in the process. W= L.atm (C) Find the change in internal energy of the gas in the process.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
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![### Adiabatic Compression of a Monatomic Ideal Gas
**Problem Statement**
Two moles of a monatomic ideal gas, such as helium, is compressed adiabatically and reversibly from a state (4.5 atm, 6.5 L) to a state with a pressure of 5 atm. For a monatomic gas, \( \gamma = \frac{5}{3} \).
1. **Volume of the Gas After Compression**
**(a)** Find the volume of the gas after compression.
\[
V_{\text{final}} = \quad \underline{\hspace{3cm}} \quad \text{L}
\]
2. **Work Done by the Gas During the Process**
**(b)** Calculate the work done by the gas in the process.
\[
W = \quad \underline{\hspace{3cm}} \quad \text{L·atm}
\]
3. **Change in Internal Energy**
**(c)** Find the change in internal energy of the gas during the process.
\[
\Delta E_{\text{int}} = \quad \underline{\hspace{3cm}} \quad \text{L·atm}
\]
4. **Check Understanding**
- What do you predict the signs of work and change in internal energy to be?
- Do the signs of work and change in internal energy match with your predictions?
---
**Additional Information for Understanding:**
- **Adiabatic Process:** An adiabatic process is one in which no heat exchange occurs between the system and its surroundings.
- **Reversible Process:** A reversible process can be reversed by an infinitesimal change without leaving any net change in either the system or the surroundings.
In an adiabatic process for an ideal gas, the following relation holds:
\[
P_1 V_1^\gamma = P_2 V_2^\gamma
\]
where \( \gamma = \frac{C_p}{C_v} \), the ratio of specific heats.
---
**Given Data:**
- Initial state: \( P_1 = 4.5 \, \text{atm}, \, V_1 = 6.5 \, \text{L} \)
- Final state: \( P_2 = 5 \, \text{atm} \)
- \( \gamma = \frac{5}{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7654f8cb-b098-4c17-82df-7ea5d6e7c2fa%2Fe7b3a8b6-0e8c-4f21-955b-71c96aae2f9b%2Frmbfh4_processed.png&w=3840&q=75)
Transcribed Image Text:### Adiabatic Compression of a Monatomic Ideal Gas
**Problem Statement**
Two moles of a monatomic ideal gas, such as helium, is compressed adiabatically and reversibly from a state (4.5 atm, 6.5 L) to a state with a pressure of 5 atm. For a monatomic gas, \( \gamma = \frac{5}{3} \).
1. **Volume of the Gas After Compression**
**(a)** Find the volume of the gas after compression.
\[
V_{\text{final}} = \quad \underline{\hspace{3cm}} \quad \text{L}
\]
2. **Work Done by the Gas During the Process**
**(b)** Calculate the work done by the gas in the process.
\[
W = \quad \underline{\hspace{3cm}} \quad \text{L·atm}
\]
3. **Change in Internal Energy**
**(c)** Find the change in internal energy of the gas during the process.
\[
\Delta E_{\text{int}} = \quad \underline{\hspace{3cm}} \quad \text{L·atm}
\]
4. **Check Understanding**
- What do you predict the signs of work and change in internal energy to be?
- Do the signs of work and change in internal energy match with your predictions?
---
**Additional Information for Understanding:**
- **Adiabatic Process:** An adiabatic process is one in which no heat exchange occurs between the system and its surroundings.
- **Reversible Process:** A reversible process can be reversed by an infinitesimal change without leaving any net change in either the system or the surroundings.
In an adiabatic process for an ideal gas, the following relation holds:
\[
P_1 V_1^\gamma = P_2 V_2^\gamma
\]
where \( \gamma = \frac{C_p}{C_v} \), the ratio of specific heats.
---
**Given Data:**
- Initial state: \( P_1 = 4.5 \, \text{atm}, \, V_1 = 6.5 \, \text{L} \)
- Final state: \( P_2 = 5 \, \text{atm} \)
- \( \gamma = \frac{5}{
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