Chapter 21, Problem 59A

What would be the final temperature if you mixed a liter of $40°C$ water with 2 liters of $20°C$ water?

To determine

Final temperature.

Answer to Problem 59A

Final temperature is, $T=26.66\text{°C}$

Explanation of Solution

Given :

Volume of water which temperature is $40°\text{C}$ is, $V_1=1\text{ L}$

Volume of water which temperature is $20°\text{C}$ is, $V_2=2\text{ L}$

Formula used :

  $Q=mc\Delta t$

Where, Q is amount of heat generated, m is mass, c is specific heat and $\Delta t$ is change in temperature.

Calculation :

Density of water is, $d=1000{\text{ kg/m}}^3$

Volume of hot water, $V_1=1\text{ L}={10}^{-3}{\text{ m}}^3$

Therefore, mass of cold water,

  $\begin{array}{c}{m}_1=d{V}_1\\ =1000\times {10}^{-3}\\ =1\text{ kg}\end{array}$

Mass of cold water,

  $\begin{array}{c}{m}_1=d{V}_2\\ =1000\times 2\times {10}^{-3}\\ =2\text{ kg}\end{array}$

According to heat transfer heat lost by hot water is equal to heat gained by cold water.

  $m_{1}c\Delta t_1=m_{2}c\Delta t_2$

Let, final temperature is $T°C$ .

Therefore,

  $\begin{array}{c}2\times c\times \left(T-20\right)=1\times c\times \left(40-T\right)\\ 2T-40=40-T\\ 3T=80\\ T=\frac{80}{3}\\ =26.66°\text{C}\end{array}$

Conclusion:

Therefore, final temperature is $26.66°\text{C}$ .