A 200 g copper pipe is heated with a Bunsen burner supplying 7410 J. If the specific heat capacity of copper is 390 J/kg°C, what is the change in temperature of the pipe (assume all energy heats the pipe) using $\Delta E = mc\Delta T$?

What you are solving for

You are given the energy added to the copper pipe, its mass, and copper’s specific heat capacity. The goal is to rearrange the heating equation to find the temperature change $\Delta T$.

Convert grams to kilograms

The specific heat capacity is in $\text{J}/(\text{kg}\,^{\circ}\text{C})$, so the mass must be in kg:

$$m = 200\,\text{g} = 0.200\,\text{kg}$$

Rearrange and substitute into $\Delta E = mc\Delta T$

Start with:

$$\Delta E = mc\Delta T$$

Solve for $\Delta T$:

$$\Delta T = \frac{\Delta E}{mc}$$

Substitute values ($\Delta E = 7410\,\text{J}$, $m=0.200\,\text{kg}$, $c=390\,\text{J}/(\text{kg}\,^{\circ}\text{C})$):

$$\Delta T = \frac{7410}{0.200\times 390} = \frac{7410}{78} = 95\,^{\circ}\text{C}$$

Quick reasonableness check

The heat capacity of the pipe is $mc = 0.200\times 390 = 78\,\text{J}/^{\circ}\text{C}$, meaning it takes $78\,\text{J}$ to raise it by $1\,^{\circ}\text{C}$. With $7410\,\text{J}$, the rise should be about $7410/78 \approx 95\,^{\circ}\text{C}$, which matches.