THE TEMPERATURE OF DIFFERENT LIQUIDS A,B and C is 12,18,28 C. Temperature of A and B mixture is 16 C. Temperature of B and C mixture is 23 C.What is the temperature of mixture of the liquids A and C?

To find the temperature of the mixture of liquids A and C, we can use the information provided about the temperatures of the individual liquids and their mixtures. Let's break this down step by step.

Understanding the Temperatures

We have three liquids with the following temperatures:

• Liquid A: 12°C
• Liquid B: 18°C
• Liquid C: 28°C

Analyzing the Mixtures

We know the temperatures of the mixtures:

• Mixture of A and B: 16°C
• Mixture of B and C: 23°C

Now, let's use these mixtures to find the temperature of the mixture of A and C.

Calculating the Mixture Temperatures

When two liquids are mixed, the temperature of the mixture can be thought of as a weighted average based on their respective temperatures and the amounts mixed. We can set up equations based on the mixtures we know.

Mixture of A and B

For the mixture of A and B, we can express the temperature of the mixture (T_AB) as:

T_AB = (m_A * T_A + m_B * T_B) / (m_A + m_B)

Given that T_AB = 16°C, T_A = 12°C, and T_B = 18°C, we can assume equal masses for simplicity (m_A = m_B = 1). Thus:

16 = (1 * 12 + 1 * 18) / (1 + 1)

16 = (12 + 18) / 2

16 = 30 / 2

16 = 15 (which is consistent, confirming our assumption of equal masses). This means the average temperature is indeed correct.

Mixture of B and C

Now, for the mixture of B and C, we can set up a similar equation:

T_BC = (m_B * T_B + m_C * T_C) / (m_B + m_C)

Given T_BC = 23°C, T_B = 18°C, and T_C = 28°C, again assuming equal masses:

23 = (1 * 18 + 1 * 28) / (1 + 1)

23 = (18 + 28) / 2

23 = 46 / 2

23 = 23 (which confirms our calculations). This is also consistent.

Finding the Temperature of Mixture A and C

Now, we need to find the temperature of the mixture of A and C. We can set up the equation:

T_AC = (m_A * T_A + m_C * T_C) / (m_A + m_C)

Assuming equal masses again:

T_AC = (1 * 12 + 1 * 28) / (1 + 1)

T_AC = (12 + 28) / 2

T_AC = 40 / 2

T_AC = 20°C

Final Result

Therefore, the temperature of the mixture of liquids A and C is 20°C.