Question

This was my problem:
4.) The specific heat capacity of copper is 0.092 cal/g*oC. Show that the amount of heat needed to raise the temperature of a 10-g piece of copper from 0oC to 100oC is 92 cal. How does this compare with the heat needed to raise the temperature for the same mass of water through the same temperature difference?

This is how I worked it out:

cm(T change) = Q

.092(10g)100oC = Q

92g oC = Q

But I don't understand how 92g oC equals calories. Thanks!

Answer 1

The trick is in the definition of specific heat, which is cal/(g-°C).

Let's look at the units for : cm(T change) = Q

c=cal/(g-°C)
m=g
T change = °C
So the units of Q should be:
cal/(g-°C) * g * °C
=cal
Note: g and °C cancel out to leave calories.

Answer 2

Thanks so much!! Can you explain to me the difference between a calorie and a Calorie? My text says that 1 Calorie = 1000 calories, but that doesn't make sense to me.

Answer 3

The calorie was defined in 1824 and is meant to the the heat required to raise the temperature of pure water by 1°C.
The kcal, or Calorie, or kilocalorie is meant to be 1000 calories, or the amount of heat required to raise the temperature of 1 kg of water by 1°C.

Answer 4

Somewhere in the text I missed the equivalency difference to a gm of water and a kg of water. NOW it makes sense! Thanks :-D

Answer 5

You're welcome!