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!
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.
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.
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
You're welcome!
Oh, don't worry! This is just a case of funny units getting in the way. Let me explain.
In this case, the "g oC" is not meant to be taken as grams multiplied by degrees Celsius. It's just a way of indicating that we're dealing with grams and degrees Celsius.
The actual unit for heat is calories (cal). So, when we multiply 92 grams by degrees Celsius, we're not getting calories—we're just keeping track of the units of mass (grams) and temperature (degrees Celsius) that we're working with.
To find the actual amount of heat in calories, we need to get rid of those pesky grams and degrees Celsius. And that's why we multiply the specific heat capacity (0.092 cal/g*oC) by the mass (10g) and the temperature change (100oC):
(0.092 cal/g*oC) * (10g) * (100oC) = 92 cal
So you see, 92g oC may seem strange, but it's just a way to keep track of the units involved. The final answer is indeed 92 calories.
As for the comparison to water, well, the specific heat capacity of water is 1 cal/g*oC. If you do the math using the same approach, you'll find that the heat needed to raise the temperature of the same mass of water through the same temperature difference is 1000 cal. So, in comparison, copper needs much less heat than water to achieve the same temperature change. Copper is a little faster when it comes to warming up!
To understand why 92 g°C equals calories, you need to understand the units involved. In this case, we have:
- Specific heat capacity (c): 0.092 cal/g*°C
- Mass (m): 10 g
- Temperature change (ΔT): 100°C
- Heat energy (Q): Unknown
Using the equation Q = mcΔT, we can substitute the given values and calculate the heat energy required:
Q = (0.092 cal/g*°C)(10 g)(100°C)
= 0.092 × 10 × 100 cal
= 92 cal
Therefore, the required heat energy to raise the temperature of a 10-g piece of copper from 0°C to 100°C is indeed 92 calories.
Now, let's compare this with the heat needed to raise the temperature of the same mass of water through the same temperature difference. The specific heat capacity of water is 1 cal/g*°C, which is significantly higher than that of copper.
Using the same equation Q = mcΔT, we can calculate the heat energy required for water:
Q = (1 cal/g*°C)(10 g)(100°C)
= 1 x 10 x 100 cal
= 1000 cal
So, for the same mass and temperature difference, it would require 1000 calories of heat energy to raise the temperature of water, compared to only 92 calories for copper.
This comparison highlights the different specific heat capacities of materials and how they affect the heat energy needed to raise the temperature of objects.
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.