Question

one litre of water at 30°c is mixed with one litre of water at 50°c. the temperature of the mixture​

Answer 1

The temperature of the mixture will be 40°C.

Let the first volume of water be V1. Let the second volume of water be V2. Let the initial temperature of the first volume of water be θ1. Let the initial temperature of the second volume of water be θ2.

Let the energy required to heat a unit volume of water by unit temperature by C.

So, if the final temperature is θfinal, we have

heat gained by the first volume of water

=V 1 ×C×(θ ffina −θ 1 )

andheat lost by the second volume of water

=V 2 ×C×(θ 2−θ ffina ).

By the law of conservation of energy,

heat lost = heat gained

∴V 1 ×C×(θ

final

−θ

1 )=V 2 ×C×(θ 2 −θ ffina )

∴V 1 θ ffina −V 1 θ 1

=V 2 θ 2 −V2 θ final

∴θ final =V 1 θ 1 +V202

V1 +V 2

Substituting the given values,

=30+50

=40∘C.