As shown in the figure, a chamber with a moveable piston and containing a monatomic ideal gas in an initial state A undergoes an isovolumetric, then an isothermal and finally an isobaric process to complete the cycle. P(atm) V(L) O When the gas is in the initial state, the volume is 3.00 L, the pressure is 5.00 atm, and the temperature is 200 K. The gas is first warmed at constant volume to a pressure of 4 times the initial value (state 8). The gas is then allowed to expand isothermally to some new volume (state C). Finally it is compressed isobarically to its initial state. (Due to the nature of th problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) Find the number of moles of the gas. moles (b) Find the temperature of the gas at state (in K). K (c) Find the temperature of the gas at state C (in K).

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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
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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