Question

One litre of water at 50°C is mixed with one litre of water at 70°C. The
temperature of the mixture will be
(a) more than 50°C but less than 7070
(b) between 50°C and 70°C
(c) 70°C
(d) 20°C​

Answer 1

One litre of water at 30oC is mixed with one litre of water at 50oC. The temperature of the mixture will be

A

80C

Your Answer

B

more than 50C but less than 80C

C

20C

D

between 30C and 50C

Correct Answer

EASY

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ANSWER

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

=V1×C×(θfinal−θ1)

and

heat lost by the second volume of water

=V2×C×(θ2−θfinal).

By the law of conservation of energy,

heat lost = heat gained

∴V1×C×(θfinal−θ1)=V2×C×(θ2−θfinal)

∴V1θfinal−V1θ1=V2θ2−V2θfina

θfinal=V1θ1+V2θ2V1+V2

Substituting the given values,

θfinal=230+50=40∘C.

The answer is option D