How do you find the final Equilibrium temperature?

Question

If 200 g of water at 100 degrees C are mixed with 300 g of water at 50 degrees C in a completely insulated container what is the final equilibrium temperature.

I would like to know the formula and any thing else need to solve this problem. Maybe an example.

Thanks Much

Answer 1

Since the container is insulated, it neither takes nor gives any heat, therefore,
suppose after mixing, the final temperature of mixed water is ' t '
Hot water gives heat to cold water,


heat taken by 300gm water at 50degree C to rise to 't'degree C is equal to heat given by 200 gram water at 100 degree C while reaching the final temperature ' t '

If S is specific heat of water ,
300 S ( t - 50 ) =200 S (100 - t )

3t - 150 = 200 - 2t

5t =350, therefore final temperature of mixture is 70 degree C