Heating Capacity from Heating Curve

[aTirumalai-1I]

Hi, I was reading the textbook, and on page 287, it says "The steeper the slope of a heating curve, the lower is the heat capacity." Can someone explain why this relationship is true?

Thanks in advance!

[Chew 2H]

Because Heating capacity refers to the amount of temperature required to raise a certain substance by 1 degree celcius, lower heat capacity means higher rise in temperature over once heated. So on the heating curve, the temperature rises higher thus making the slope of the curve steeper.

[mitalisharma2B]

A steeper slope on a heating curve is indicative of a greater temperature change over a lesser energy expenditure. Heat capacity relates to the amount of energy required to increase the temperature by 1 degree Celsius.

A lower heat capacity will correlate to a steeper slope because it the temperature can be raised much more (high y value) for the same amount of energy (x value) as in a part of the graph with a less steep slope.

In other words, less energy (lower heat capacity) can be used to raise the temperature to the same level as a less steep part of the heating curve.