Chapter 12, Problem 104E

Interpretation Introduction

Interpretation: The final temperature of the entire water sample is to be determined.

Concept Introduction: The amount of heat required to raise the temperature by $1°C$ of a substance is called heat capacity of that substance.

Heat capacity of water is $4.18\text{ J/g}°C$.

The relation between heat $\left(q\right)$, mass $\left(m\right)$, heat capacity $\left(C\right)$ and change in temperature $\left(\Delta T\right)$ is:

$q=m.C.\Delta T$ …… (1)

When condensation of steam takes place in an insulated container then there is no loss of heat in the surroundings. Thus, heat released is equal to heat gained.

$-q_{\text{s}}=q_{\text{w}}$

Here, $-q_{\text{s}}$ is the amount of heat released during condensation and $q_{\text{w}}$ is the amount of heat gained by water molecules. The negative sign indicates that heat is released during the condensation.