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This problem is about heat transfer between two materials with different specific heat capacities and temperatures. Here’s the step-by-step solution:

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Let:
- \( m_A = 2 \, \text{kg} \) (mass of substance A)
- \( c_A = 800 \, \text{J} \, \text{kg}^{-1} \, ^\circ\text{C}^{-1} \) (specific heat capacity of substance A)
- \( T_A = 30^\circ\text{C} \) (initial temperature of A)

- \( m_B = 4 \, \text{kg} \) (mass of substance B)
- \( c_B = 500 \, \text{J} \, \text{kg}^{-1} \, ^\circ\text{C}^{-1} \) (specific heat capacity of substance B)
- \( T_B = 60^\circ\text{C} \) (initial temperature of B)

Let the final equilibrium temperature be \( T \).

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### Step 1: Set up the heat balance equation

Since no heat is lost to the surroundings, the heat gained by one substance will be equal to the heat lost by the other:

\[
m_A c_A (T - T_A) = m_B c_B (T_B - T)
\]

### Step 2: Substitute values into the equation

\[
2 \times 800 \times (T - 30) = 4 \times 500 \times (60 - T)
\]

Simplify:

\[
1600 (T - 30) = 2000 (60 - T)
\]

### Step 3: Expand and solve for \( T \)

\[
1600T - 48000 = 120000 - 2000T
\]

Combine like terms:

\[
3600T = 168000
\]

\[
T = \frac{168000}{3600} = 46.67^\circ\text{C}
\]

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### Answer

The final equilibrium temperature \( T \) is approximately \( 46.67^\circ\text{C} \).

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Would you like a detailed explanation of each step?

Here are some related questions:

1. How is specific heat capacity used in heat transfer calculations?
2. What are the assumptions made in the heat balance equation?
3. How would the answer change if the masses of substances A and B were different?
4. Can this formula be applied to materials undergoing a phase change?
5. How does heat capacity differ from specific heat capacity?

**Tip:** Always check the units for consistency in physics calculations, especially when dealing with specific heat and temperature changes.

විශිෂ්ට කාප ධාරිතාව 800Jkg⁻¹°C⁻¹ වන 30°C ක උෂ්ණත්වයේ පවතින A නමැති ද්‍රවය 2kgක්, විශිෂ්ට කාප ධාරිතාව 500Jkg⁻¹°C⁻¹ වන 60°C ක උෂ්ණත්වයේ B නමැති ද්‍රවය 4kgක් සමග මිශ්‍ර කරනු ලැබේ. පසුවයෙන් සමග තාප හුවමාරුවක් සිදු වන විට එම මින්ෂාක තාපීත උෂ්ණත්වය සොයන්න.

This problem involves calculating the equilibrium temperature when a 2kg substance at 30°C with a specific heat capacity of 800 J/kg°C is mixed with a 4kg substance at 60°C with a specific heat capacity of 500 J/kg°C. Learn the step-by-step solution using heat transfer principles and energy conservation.

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