Question

What would be the final temperature of a mixture of $50g$ of water at ${20}^{o}C$ temperature and $50g$ of water at ${40}^{o}C$ temperature?

Answer 1

Let the final temperature be = T ⁰C

Amount of heat given out by the hot water = m * s * (40⁰C - T) = 50 gms * s* (40 -T)

Amount of heat taken in by the cold water = m * s * (T - 20⁰C) = 50 gms * s * (T - 20 )

As the amounts are equal and the heat is transferred from hot water to cold water without any loss of heat to any surroundings, therefore,

Heat loss = Heat gain

$\Rightarrow 50\times s\times (40-T)=50\times s\times (T-20)\Rightarrow 40-T=T-20\Rightarrow 2T=60\Rightarrow T=30℃$.