### Thermodynamics Problem: Gas Pressure in an Insulated Container#### Problem StatementA beaker with a metal bottom is filled with 17 g of water at 20 °C. It is brought into good thermal contact with a 4000 cm³ container holding 0.50 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings.![Figure 1](pathway/to/image)**Figure 1:**- **Description:** - The diagram shows a water-filled beaker mounted above a container with gas. - The water is separated from the gas by a thin metal layer, facilitating heat transfer. - Both the beaker and the gas container are enclosed with insulation to ensure no heat exchange with the surroundings.#### TaskDetermine the gas pressure after a long time has elapsed. You can assume that the containers themselves are nearly massless and do not affect the outcome.#### SolutionTo find the final pressure of the gas, use the principle of conservation of energy. Here's the step-by-step approach:1. **Conservation of Energy:** - The heat lost by the gas equals the heat gained by the water. 2. **Heat Transfer Equation:** - \( Q = nC_v\Delta T \) for the gas, where \( Q \) is the heat, \( n \) is the number of moles, \( C_v \) is the specific heat capacity, and \( \Delta T \) is the temperature change. - \( Q = mC_w\Delta T \) for the water, where \( m \) is the mass, \( C_w \) is the specific heat capacity, and \( \Delta T \) is the temperature change.3. **Ideal Gas Law:** - \( PV = nRT \)4. **Heat Exchange:** - Let \( T_f \) be the final temperature for both the gas and the water after thermal equilibrium is reached.5. **Expressing the Final Pressure:** - Relate the final temperature back to the pressure using the ideal gas law.**Work through the equations carefully to solve for the final pressure, `p`, and ensure to express your answer in appropriate units. Provide inputs where needed, such as specific heat capacities and conversion constants.***Note: This problem involves a detailed step-by-step approach to reach the solution. If any steps are

A beaker with a metal bottom is filled with 17 g of water at 20 °C. It is brought into good thermal contact with a 4000 cm³ container holding 0.50 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings. (Figure 1) Figure Insulation Water Gas 1 of 1 > Thin metal What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome. Express your answer with the appropriate units. p= Value Submit Provide Feedback A Request Answer Units Big 11 ? Next >

A beaker with a metal bottom is filled with 17 g of water at 20 °C. It is brought into good thermal contact with a 4000 cm³ container holding 0.50 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings. (Figure 1) Figure Insulation Water Gas 1 of 1 > Thin metal What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome. Express your answer with the appropriate units. p= Value Submit Provide Feedback A Request Answer Units Big 11 ? Next >

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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Concept explainers

Kinetic Theory of Gas

The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.

P-V Diagram

A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.

Question

### Thermodynamics Problem: Gas Pressure in an Insulated Container

#### Problem Statement
A beaker with a metal bottom is filled with 17 g of water at 20 °C. It is brought into good thermal contact with a 4000 cm³ container holding 0.50 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings.

![Figure 1](pathway/to/image)

**Figure 1:**
- **Description:**
- The diagram shows a water-filled beaker mounted above a container with gas.
- The water is separated from the gas by a thin metal layer, facilitating heat transfer.
- Both the beaker and the gas container are enclosed with insulation to ensure no heat exchange with the surroundings.

#### Task
Determine the gas pressure after a long time has elapsed. You can assume that the containers themselves are nearly massless and do not affect the outcome.

#### Solution
To find the final pressure of the gas, use the principle of conservation of energy. Here's the step-by-step approach:

1. **Conservation of Energy:**
- The heat lost by the gas equals the heat gained by the water.

2. **Heat Transfer Equation:**
- \( Q = nC_v\Delta T \) for the gas, where \( Q \) is the heat, \( n \) is the number of moles, \( C_v \) is the specific heat capacity, and \( \Delta T \) is the temperature change.
- \( Q = mC_w\Delta T \) for the water, where \( m \) is the mass, \( C_w \) is the specific heat capacity, and \( \Delta T \) is the temperature change.

3. **Ideal Gas Law:**
- \( PV = nRT \)

4. **Heat Exchange:**
- Let \( T_f \) be the final temperature for both the gas and the water after thermal equilibrium is reached.

5. **Expressing the Final Pressure:**
- Relate the final temperature back to the pressure using the ideal gas law.

**Work through the equations carefully to solve for the final pressure, `p`, and ensure to express your answer in appropriate units. Provide inputs where needed, such as specific heat capacities and conversion constants.**

*Note: This problem involves a detailed step-by-step approach to reach the solution. If any steps are

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