Three liquids A, B and C having same specific heat and mass , 2m and 3m have temperatures `20^(@)C, 40^(@)C` and `60^(@)C` respectively. Temperature of the mixture when
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Answer

To find the temperature of the mixture of three liquids A, B, and C, we can use the principle of conservation of energy. The heat lost by the hotter liquids will be equal to the heat gained by the cooler liquids.

### Step-by-Step Solution:

1. **Identify the Masses and Temperatures:**
- Liquid A: Mass = 2m, Temperature = 20°C
- Liquid B: Mass = 3m, Temperature = 40°C
- Liquid C: Mass = m, Temperature = 60°C

2. **Set Up the Heat Balance Equation:**
When the three liquids are mixed, the heat gained by the cooler liquids must equal the heat lost by the warmer liquids. We can set up the equation based on the specific heat capacity (which is the same for all liquids) and the temperatures.

\[ \text{Heat gained by A and B} = \text{Heat lost by C} \]

\[ (2m)(T - 20) + (3m)(T - 40) = (m)(60 - T) \]

3. **Simplify the Equation:**
We can simplify the equation by canceling out the mass (m) from all terms since it is common:

\[ 2(T - 20) + 3(T - 40) = 60 - T \]

4. **Distribute and Combine Like Terms:**
Expanding the left side:

\[ 2T - 40 + 3T - 120 = 60 - T \]

Combine like terms:

\[ 5T - 160 = 60 - T \]

5. **Rearranging the Equation:**
Add T to both sides:

\[ 6T - 160 = 60 \]

Now, add 160 to both sides:

\[ 6T = 220 \]

6. **Solve for T:**
Divide both sides by 6:

\[ T = \frac{220}{6} \approx 36.67°C \]

### Final Temperature of the Mixture:
The final temperature of the mixture when liquids A, B, and C are combined is approximately **36.67°C**.

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