Question

Use the heat equation to find out how many joules of energy are needed

Answer 1

Answer:

About 7.0 × 10³ J or 7.0 kJ

Explanation:

We want to determine the amount of energy needed to raise the temperature of 67 grams of water from 20°C to 45°C.

We can use the heat equation:

$\displaystyle q = mC\Delta T$

Where C is the specific heat of water.

Substitute and evaluate:

$\displaystyle \begin{aligned} q & = (67\text{ g})\left(\frac{4.2\text{ J}}{\text{g- ^\circ C}}\right)\left(45^\circ \text{ C}- 20.^\circ\text{ C}\right) \\ \\ & = (67\text{ g})\left(\frac{4.2\text{ J}}{\text{g- ^\circ C}}\right)(25^\circ \text{ C}) \\ \\ & = 7.0\times 10^3 \text{ J}\end{aligned}$

Recall that there are 1000 J in a kJ. Hence:

$\displaystyle \begin{aligned} q & = 7.0\times 10^3 \text{ J} \cdot \frac{1\text{ kJ}}{1000\text{ J}} \\ \\ & = 7.0 \text{ kJ}\end{aligned}$

In conclusion, it will take about 7.0 × 10³ J or 7.0 kJ of energy to raise the temperature of 67 grams of water from 20 °C to 45 °C.