Using the equation change in thermal energy = mass × specific heat capacity × change in temperature, some bath water requires 5670 kJ to increase its temperature by 15°C. If the specific heat capacity of water is 4200 J/kg°C, what is the mass of water?

What you are being asked to find

You are given the energy added to the water, the temperature rise, and water’s specific heat capacity. The goal is to rearrange the heating equation to solve for the mass.

Convert the energy into joules

The specific heat capacity is in $\text{J/(kg°C)}$, so $Q$ must be in joules:

$$5670\,\text{kJ} = 5670\times 1000\,\text{J} = 5{,}670{,}000\,\text{J}$$

Rearrange $Q = mc\Delta T$ to make $m$ the subject

Start with:

$$Q = mc\Delta T$$

Solve for $m$ by dividing both sides by $c\Delta T$:

$$m = \frac{Q}{c\Delta T}$$

Substitute values and calculate

$$m = \frac{5{,}670{,}000}{4200\times 15}$$

Compute the denominator:

$$4200\times 15 = 63{,}000$$

Then:

$$m = \frac{5{,}670{,}000}{63{,}000} = 90\,\text{kg}$$

So the bath contains $90\,\text{kg}$ of water (about $90\,\text{L}$, since water is about $1\,\text{kg/L}$).