Question

A 150 L 1≈40 gal2 electric hot-water tank has a 5.0 kW heater.

How many minutes will it take to raise the water temperature from 65°F to 140°F?

Short answer

The required time is 87mins

Step-by-step solution

Definition of temperature

Temperature is measured of coldness and hotness that is account wit different scales.

Finding the time

The temperature difference is ${75}^{o}F$that is in kelvin $41.\overline{6}K$

Assume Q is heart and t is time so $P=\frac{Q}{t}$

where P is power

$m=\rho V$

Now $$\begin{gathered} t=\left(\frac{cm∆T}{P}\right)=\left(\frac{\rho cV∆T}{P}\right) \\ =\left(\frac{1000\times 4190\times 0.150\times 41.\overline{6}}{5000}\right)=5237.5s \end{gathered}$$

Now convert second in minutes$\left(\frac{5237.5}{60}\right)=87mins$