### Heat curve

Posted:

**Thu Mar 15, 2018 7:06 pm**The steeper the slope of a heat curve, the smaller the heat capacity is? can someone provide also provide a mathematical example to prove/disprove my statement as well.

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=77&t=29866

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Posted: **Thu Mar 15, 2018 7:06 pm**

The steeper the slope of a heat curve, the smaller the heat capacity is? can someone provide also provide a mathematical example to prove/disprove my statement as well.

Posted: **Thu Mar 15, 2018 7:24 pm**

Yes that would be correct! If we look at a heating curve, the x-axis would be the heat absorbed and the y-axis would be the temperature.

Let's say for some substance, the heat capacity of a substance in a solid phase is 10 J/^{o}C and the heat capacity of the same substance is 20 J/^{o}C in its liquid phase.

Slope would be equal to (change in temperature/change in heat absorbed)

The slope of the heat curve in the solid phase would be 1/10 while the slope of the heat curve in the liquid phase would be 1/20.

1/10 > 1/20 thus meaning it has a steeper slope which makes sense because it corresponds with the lower heat capacity.

Let's say for some substance, the heat capacity of a substance in a solid phase is 10 J/

Slope would be equal to (change in temperature/change in heat absorbed)

The slope of the heat curve in the solid phase would be 1/10 while the slope of the heat curve in the liquid phase would be 1/20.

1/10 > 1/20 thus meaning it has a steeper slope which makes sense because it corresponds with the lower heat capacity.

Posted: **Thu Mar 15, 2018 7:35 pm**

Conceptually, if a metal has a lower specific heat, it should take less time to get to the same temperature as a metal with a higher one, giving it a steeper slope.