7.) Two blocks of Cu, one mass 100 g and the other mass 150 g, are placed in thermal contact with one another in an adiabatic chamber, such that no heat can escape. If the 100 g piece is initially at 300 K and the 150 g piece is 400 K, then what is the final equilibrium temperature of the system? (note: Cp for Cu = 0.386 J/g K, also the heat lost by one will be gained by the other)

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**Educational Content on Thermal Equilibrium in an Adiabatic Chamber**

**Scenario:** Two blocks of copper (Cu), one with a mass of 100 g and the other with a mass of 150 g, are placed in thermal contact inside an adiabatic chamber where no heat can escape. The 100 g piece starts at 300 K and the 150 g piece at 400 K. We aim to find the final equilibrium temperature of the system.

**Given:**
- Specific heat capacity \( C_p \) for Cu: 0.386 J/g·K
- \( q = 0 \) (adiabatic condition: heat lost by one is gained by the other)

**Formulas:**
- Final temperature \( T_f \): 
  \[
  T_f = T_i \left(\frac{v_i}{v_f}\right)^{\frac{1}{c}}
  \]
- Specific heat formula:
  \[
  c = \frac{C_v m}{R}
  \]

**Diagram Explanation:**
The diagram on the right visualizes the thermal contact of the two copper pieces:
- A smaller rectangle represents the 100 g block at 300 K.
- A larger rectangle represents the 150 g block at 400 K.
- Both blocks are enclosed within a larger rectangle symbolizing the adiabatic chamber.

**Key Concepts:**
- **Adiabatic Process**: A process where no heat is transferred into or out of the system.
- **Thermal Equilibrium**: Achieved when two objects in thermal contact reach the same temperature, with no net heat flow between them.

This example illustrates the principle of energy conservation and thermal dynamics in a closed system.
Transcribed Image Text:**Educational Content on Thermal Equilibrium in an Adiabatic Chamber** **Scenario:** Two blocks of copper (Cu), one with a mass of 100 g and the other with a mass of 150 g, are placed in thermal contact inside an adiabatic chamber where no heat can escape. The 100 g piece starts at 300 K and the 150 g piece at 400 K. We aim to find the final equilibrium temperature of the system. **Given:** - Specific heat capacity \( C_p \) for Cu: 0.386 J/g·K - \( q = 0 \) (adiabatic condition: heat lost by one is gained by the other) **Formulas:** - Final temperature \( T_f \): \[ T_f = T_i \left(\frac{v_i}{v_f}\right)^{\frac{1}{c}} \] - Specific heat formula: \[ c = \frac{C_v m}{R} \] **Diagram Explanation:** The diagram on the right visualizes the thermal contact of the two copper pieces: - A smaller rectangle represents the 100 g block at 300 K. - A larger rectangle represents the 150 g block at 400 K. - Both blocks are enclosed within a larger rectangle symbolizing the adiabatic chamber. **Key Concepts:** - **Adiabatic Process**: A process where no heat is transferred into or out of the system. - **Thermal Equilibrium**: Achieved when two objects in thermal contact reach the same temperature, with no net heat flow between them. This example illustrates the principle of energy conservation and thermal dynamics in a closed system.
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