1. Sep 13, 2014

fabrc

Quantity of heat (Q) is directly proportional to specific heat (C)?

I thought that they would be inversely proportional because the higher the value of C, more heat is necessary to make a variation of temperature but somehow it seems wrong.

Thanks!

2. Sep 13, 2014

Staff: Mentor

The amount of heat needed to produce a temperature change of $\Delta{T}$ in a mass of $m$ of a substance with specific heat $C$ is given by $\Delta{Q}=mC\Delta{T}$, right? The higher the value of $C$, the more heat will be necessary, just as you say. That's a direct proportionality relationship by definition . An inversely proportional relationship would have either $C$ or $\Delta{T}$ in the denominator of a fraction.

Another example: travel time is directly proportional to distance and inversely proportional to speed (all else being the same, the greater the distance the greater the travel time and the greater the speed the less the travel time). These quantities are related by $T=d/s$ where $T$ is the travel time, $d$ is the distance traveled, and $s$ is the speed. Look at which one appears in the denominator of a fraction.

3. Sep 14, 2014

fabrc

I got it. Thanks, Nugatory!