Question

If 5 L of water at 50°C is mixed with 4L of water at 30°C, what will be the final temperature of water?
Take the specific heat capacity of water as 4184 J kg^-1 K^-1.

Answer 1

Answer:

Use the “lever rule” or method of moments. Imagine they are weights on either end of a beam and you have to have a fulcrum to balance. Obviously the 1 litre should be 5 times as far away from the fulcrum as the 5 litre. That is, the fulcrum is 5/6 of the way from the l liter to the 5 litre.

The length between them is 20 degrees, so the fulcrum is 5/6 x 20 degrees from the temperature of the 1 litre towards the temperature of the 5 litre.

In this case, it is 30 + 16.67 degrees.

Works for other kinds of mixing, including concentrations.

E.g. if we had 1 litre of 30 g/l and 5 litres of 50 g/l, the concentration would be 46.67 g/l.

Very quick, easy and handy thing to know in chemistry.