5. Block A has a heat capacity of 800J/K and starts 15°C; block B has a heat capacity of 300J/K and starts at 40°C. The two blocks are placed next to each other and reach thermal equilibrium. a) What is the final temperature of the two blocks, when they reach thermal equilibrium? A C = 800J/K T₁ = 15°C at b) How much heat flows between the blocks, and in which direction? B C = 300J/K T₁ = 40°C

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**Problem Statement:**

5. Block A has a heat capacity of 800 J/K and starts at 15°C; block B has a heat capacity of 300 J/K and starts at 40°C. The two blocks are placed next to each other and reach thermal equilibrium.

a) What is the final temperature of the two blocks when they reach thermal equilibrium?

b) How much heat flows between the blocks, and in which direction?

**Diagram:**

- There are two labeled blocks, A and B.
  - **Block A**: 
    - Heat capacity (C) = 800 J/K
    - Initial temperature (T₁) = 15°C
  - **Block B**: 
    - Heat capacity (C) = 300 J/K
    - Initial temperature (T₁) = 40°C

**Analysis:**

To solve for the final temperature and heat flow:

- Use the principle of conservation of energy where the heat lost by one block is equal to the heat gained by the other block.
- Set up the equation using the heat capacity formula: 
  \[
  (C_A)(T_f - T_{iA}) = -(C_B)(T_f - T_{iB})
  \]
  where \( T_f \) is the final equilibrium temperature, \( T_{iA} \) and \( T_{iB} \) are the initial temperatures of blocks A and B, and \( C_A \) and \( C_B \) are their respective heat capacities.

- Rearrange the equation to solve for \( T_f \).

- Calculate the heat flow using the formula:
  \[
  Q = C \times (T_f - T_i)
  \]
  Determine the direction of heat flow by assessing the sign of \( Q \).

Use this information to compute the final temperature and detail the heat transfer between the two blocks.
Transcribed Image Text:**Problem Statement:** 5. Block A has a heat capacity of 800 J/K and starts at 15°C; block B has a heat capacity of 300 J/K and starts at 40°C. The two blocks are placed next to each other and reach thermal equilibrium. a) What is the final temperature of the two blocks when they reach thermal equilibrium? b) How much heat flows between the blocks, and in which direction? **Diagram:** - There are two labeled blocks, A and B. - **Block A**: - Heat capacity (C) = 800 J/K - Initial temperature (T₁) = 15°C - **Block B**: - Heat capacity (C) = 300 J/K - Initial temperature (T₁) = 40°C **Analysis:** To solve for the final temperature and heat flow: - Use the principle of conservation of energy where the heat lost by one block is equal to the heat gained by the other block. - Set up the equation using the heat capacity formula: \[ (C_A)(T_f - T_{iA}) = -(C_B)(T_f - T_{iB}) \] where \( T_f \) is the final equilibrium temperature, \( T_{iA} \) and \( T_{iB} \) are the initial temperatures of blocks A and B, and \( C_A \) and \( C_B \) are their respective heat capacities. - Rearrange the equation to solve for \( T_f \). - Calculate the heat flow using the formula: \[ Q = C \times (T_f - T_i) \] Determine the direction of heat flow by assessing the sign of \( Q \). Use this information to compute the final temperature and detail the heat transfer between the two blocks.
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