College Physics
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Author: Raymond A. Serway, Chris Vuille
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![**Analyzing Thermodynamic Processes in a Monatomic Ideal Gas**
**Introduction:**
The figure below represents a chamber with a moveable piston containing a monatomic ideal gas initially at state A. The gas undergoes three types of thermodynamic processes: isochoric, isothermal, and isobaric, completing a cycle.
**Graph Description:**
The graph presented plots pressure (P) in atm against volume (V) in liters. Three states of the gas (A, B, and C) are marked:
- **A:** Initial state at (V=3.00 L, P=5.00 atm, T=200 K)
- **B:** Intermediate state
- **C:** Final state completing the cycle
From state A to B, volume remains constant (isochoric process) while the pressure increases. From state B to C, the gas expands isothermally and then returns to the initial state A through an isobaric process.
**Problem Information and Steps:**
**Initial Conditions:**
- Volume at state A (VA): 3.00 L
- Pressure at state A (PA): 5.00 atm
- Temperature at state A (TA): 200 K
**Process Details:**
1. The gas is heated at constant volume (isochoric) up to a pressure that is 4 times the initial pressure (PB = 4 * 5.00 atm = 20.00 atm).
2. The gas then undergoes isothermal expansion to a new volume (VC).
3. Finally, the gas is compressed isobarically to return to original state A.
**Tasks:**
(a) **Find the number of moles of the gas.**
Given the initial conditions and using the ideal gas law \( PV = nRT \) where R is the universal gas constant:
- PA = 5.00 atm
- VA = 3.00 L
- TA = 200 K
- R = 0.0821 atm·L/(mol·K)
- Calculate n (number of moles)
(b) **Find the temperature of the gas at state B (TB in K).**
- Volume remains constant (isochoric process), therefore:
\[ T_B = \frac{T_A \cdot P_B}{P_A} \]
- Calculate TB
(c) **Find the temperature of the gas at state C (TC in](https://content.bartleby.com/qna-images/question/7f7b26af-ddfa-4bbd-a5e5-64da57ec1d7a/38ffc4e1-7703-44a0-a977-02923e679917/ezdd8s_processed.png)
Transcribed Image Text:**Analyzing Thermodynamic Processes in a Monatomic Ideal Gas**
**Introduction:**
The figure below represents a chamber with a moveable piston containing a monatomic ideal gas initially at state A. The gas undergoes three types of thermodynamic processes: isochoric, isothermal, and isobaric, completing a cycle.
**Graph Description:**
The graph presented plots pressure (P) in atm against volume (V) in liters. Three states of the gas (A, B, and C) are marked:
- **A:** Initial state at (V=3.00 L, P=5.00 atm, T=200 K)
- **B:** Intermediate state
- **C:** Final state completing the cycle
From state A to B, volume remains constant (isochoric process) while the pressure increases. From state B to C, the gas expands isothermally and then returns to the initial state A through an isobaric process.
**Problem Information and Steps:**
**Initial Conditions:**
- Volume at state A (VA): 3.00 L
- Pressure at state A (PA): 5.00 atm
- Temperature at state A (TA): 200 K
**Process Details:**
1. The gas is heated at constant volume (isochoric) up to a pressure that is 4 times the initial pressure (PB = 4 * 5.00 atm = 20.00 atm).
2. The gas then undergoes isothermal expansion to a new volume (VC).
3. Finally, the gas is compressed isobarically to return to original state A.
**Tasks:**
(a) **Find the number of moles of the gas.**
Given the initial conditions and using the ideal gas law \( PV = nRT \) where R is the universal gas constant:
- PA = 5.00 atm
- VA = 3.00 L
- TA = 200 K
- R = 0.0821 atm·L/(mol·K)
- Calculate n (number of moles)
(b) **Find the temperature of the gas at state B (TB in K).**
- Volume remains constant (isochoric process), therefore:
\[ T_B = \frac{T_A \cdot P_B}{P_A} \]
- Calculate TB
(c) **Find the temperature of the gas at state C (TC in
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