Two substances have the same mass and are both initially at 200°C. They both absorb 150 J of energy. Which substance will have the higher temperature, the one with the higher or the lower specific heat?

Jan 3, 2016

The one with the lower specific heat.

Explanation:

A substance's specific heat tells you how much heat must be added to / removed from a $\text{1-g}$ sample of this substance in order to get its temperature to change by ${1}^{\circ} \text{C}$.

When energy in the form of heat is absorbed, a substance's specific heat tells you exactl;y how much heat is needed in order to increase the temperature of $\text{1 g}$ of this substance by ${1}^{\circ} \text{C}$.

This means that the higher the specific heat of a substance, the more heat will be needed in order to get the temperature of $\text{1 g}$ to increase by ${1}^{\circ} \text{C}$.

In your case, two substances, let's say $A$ and $B$, start at the temperature, ${200}^{\circ} \text{C}$ and they both absorb $\text{150 J}$ of heat. Moreover, they both have the same mass.

If the specific heat of $A$ is higher than the specific heat of $B$, you can say that it will take more energy to raise the temperature of $A$ by ${1}^{\circ} \text{C}$ than to raise the temperature of $B$ by ${1}^{\circ} \text{C}$.

So, if $B$ absorbs $\text{150 J}$ and gets to a final temperature ${T}_{B}$, the fact that $A$ has a higher specific heat will tell you that absorbing $\text{150 J}$ of heat will not get the final temperature of $A$, ${T}_{A}$, to the same value as ${T}_{B}$.

You can thus say that

${T}_{A} < {T}_{B}$

The substance with the lower specific heat will heat up more than the substance with the higher specific heat.