To solve the problem regarding the mixing of liquids A, B, and C at different temperatures, we can use the principle of conservation of energy, specifically the concept of heat transfer. When two substances at different temperatures are mixed, heat will flow from the hotter substance to the cooler one until thermal equilibrium is reached. Let's break down the problem step by step.

Understanding the Given Temperatures

We have three liquids with the following temperatures:

• Liquid A: 10°C
• Liquid B: 25°C
• Liquid C: 40°C

Mixing A and B

When liquids A and B are mixed, the resulting temperature is 15°C. This indicates that heat is transferred from B (the hotter liquid) to A (the cooler liquid). The heat lost by B equals the heat gained by A.

Mixing B and C

Next, when liquids B and C are mixed, the resulting temperature is 30°C. Again, heat flows from C to B, as C is hotter than B. This gives us another relationship between the temperatures.

Finding the Temperature of A and C Mixture

Now, we need to find the temperature when liquids A and C are mixed. To do this, we can use the information we have from the previous mixtures.

Using the Heat Transfer Concept

For the mixture of A and C, we can denote the final temperature as T. Since A is at 10°C and C is at 40°C, we can set up the equation based on the principle of heat transfer:

Heat lost by C = Heat gained by A

In terms of temperature, this can be expressed as:

• m_C * (T_C - T) = m_A * (T - T_A)

Assuming equal masses (m_A = m_C), we can simplify this to:

• (T_C - T) = (T - T_A)

Substituting the Values

Substituting the known temperatures:

• T_C = 40°C
• T_A = 10°C

This gives us:

• (40 - T) = (T - 10)

Solving for T

Now, let's solve for T:

• 40 - T = T - 10
• 40 + 10 = 2T
• 50 = 2T
• T = 25°C

Final Temperature of A and C Mixture

Therefore, when liquids A and C are mixed, the resulting temperature will be 25°C. This temperature makes sense as it is the average of the two temperatures, considering equal masses and the heat transfer principles we applied.

In summary, the temperature of the mixture of liquids A and C is 25°C. This approach illustrates how we can use basic principles of thermodynamics to solve problems involving heat transfer and temperature changes in mixtures.