Question

Equal masses of three liquids A,B and Chave temperatures 10 ∘ C,25 ∘C and 40 ∘ C respectively. If A and B are mixed, the mixture has a temperature of 15 ∘C. If B and C are mixed, the mixture has a temperature of 30 ∘C. If A and C are mixed the temperature of the mixture is:

A 29°C
B 25°C
C 20°C
D 16°C

Answer 1

When A and C are mixed, the temperature of the mixture cannot be determined without knowing the specific heat capacities and masses of the liquids.

Step-by-step explanation:

To find the temperature when A and C are mixed, we can apply the principle of heat transfer. When two substances at different temperatures are mixed, the heat lost by one substance is equal to the heat gained by the other substance. In this case, A is at 10°C and C is at 40°C, so the heat lost by A is equal to the heat gained by C. Let's calculate:

1. Heat lost by A = mass of A * specific heat capacity of A * change in temperature of A = mass of A * specific heat capacity of A * (Tfinal - Tinitial)
2. Heat gained by C = mass of C * specific heat capacity of C * change in temperature of C = mass of C * specific heat capacity of C * (Tfinal - Tinitial)
3. Since the heat lost is equal to the heat gained, we can equate the two equations and solve for Tfinal:
4. mass of A * specific heat capacity of A * (Tfinal - Tinitial) = mass of C * specific heat capacity of C * (Tfinal - Tinitial)
5. Cancelling out the common factors, we get:
6. Tfinal - Tinitial = (mass of C * specific heat capacity of C) / (mass of A * specific heat capacity of A)
7. Plugging in the given values:
8. Tfinal - 10 = (mass of C * specific heat capacity of C) / (mass of A * specific heat capacity of A)
9. Tfinal = (mass of C * specific heat capacity of C) / (mass of A * specific heat capacity of A) + 10

So, the temperature of the mixture when A and C are mixed is given by the formula Tfinal = (mass of C * specific heat capacity of C) / (mass of A * specific heat capacity of A) + 10. We don't have the specific heat capacities or masses of the liquids, so we cannot determine the exact temperature. Therefore, the correct answer is cannot be determined.