Question

What could be the final temperature of a mixture of $100{\text{ }}g$ of water at ${90^ \circ }{\text{ }}C$ and $600{\text{ }}g$ of water at ${20^ \circ }{\text{ }}C$?

Answer 1

We cannot just put the mean of the two temperatures to find the answer. We have to use the Law of Calorimetry to find the answer. The heat lost by one body is equal to the heat gained by the other body. We will use this principle to find the answer.

Complete step by step answer:
In this type of question, we have to use the Law of Calorimetry, which states that the heat that is lost by one body is gained by the other body.It is given by the formula,
$Q = ms\Delta T$
where $Q =$ the amount of heat lost or gained, $m =$ mass of the body, $s =$ specific heat of the body and $\Delta T =$ change in temperature of the body.

The specific heat in the given question is constant as it is dependent on different substances.As both the medium is water, then their specific heat is the same.Let the temperature of the mixture is $T$.Using Calorimetry formula we get,
The heat lost$=$ The heat gained
$100 \times s \times \left( {90 - T} \right) = 600 \times s \times \left( {T - 20} \right)$
By solving the given equation, we get to know that,
$\therefore T = {30^ \circ }{\text{ }}C$

Thus, the final temperature of the mixture is ${30^ \circ }{\text{ }}C$.

Note: It must be noted that in this type of question as the masses are different the final temperature of the mixture is not the mean of the two temperatures. If a mixture is having the same substance of the same mass then the mean of two temperatures is said to be the final temperature. Specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree.