Chapter 11, Problem 1P

To determine

Find the final temperature of water.

Answer to Problem 1P

The final temperature of water is $\underset{¯}{20.23°\text{C}}$.

Explanation of Solution

Given information:

The mass of one cubic meter water $\left(m\right)$ is $1,000\text{kg}$.

The vertical height $\left(h\right)$ is $100\text{m}$.

The initial temperature $\left(T_0\right)$ is $20°\text{C}$

Calculation:

Take the gravitational constant $\left(g\right)$ as $\text{9}\text{.8}{\text{m/s}}^{\text{2}}$.

Find the potential energy at the height h $\left(E\right)$ as follows:

$\begin{array}{c}E=mgh\\ =1,000\text{kg}\times \text{9}\text{.8}{\text{m/s}}^{\text{2}}\times 100\text{m}\\ =\text{98}\times {\text{10}}^4\text{J}\end{array}$

Take the specific heat of water $\left(C\right)$ as $4,186\text{J/kg}°\text{C}$.

Calculate the change in temperature $\left(\Delta T\right)$ as follows:

$\begin{array}{c}\Delta T=\frac{E}{mC}\\ =\frac{\text{98}\times {\text{10}}^4\text{J}}{1,000\text{kg}\times 4,186\text{J/kg}°\text{C}}\\ =0.23°\text{C}\end{array}$

Find the final temperature of water $\left(T\right)$ as follows:

$\begin{array}{c}T=T_0+\Delta T\\ =20°\text{C}+0.23°\text{C}\\ =20.23°\text{C}\end{array}$

Therefore, the final temperature of water is $\underset{¯}{20.23°\text{C}}$.