# Amount of heat = 80 kJ -- how much ice can you melt?

• Yeahaight
In summary: You got to be kidding. If you have $1.00 dollar, and each item costs 20 cents ($0.20), how many items can you buy?
Yeahaight
Homework Statement
How much ice at a temperature of -10°C can be melted and the resulting water heated to 20°C using 80 kJ of heat?
Given values:
t1 = 10°C
t2 = 20°C
Q = 80kJ
specific heat of fusion = 3,34*10^5 J/kg
c of ice = 2,2*10^3 J/kg * K
c of water = 4,2*10^3 J/kg * K
Relevant Equations
Q = cm(t2-t1)=cmΔt
I've been messing with the Q = cm(t2-t1)=cmΔt formula
If I change it to m=Q/(c*Δt) everything is fine until I reach the c part, because there has been given the c of ice and the c of water too, do I just subtract c ice from c water?

Yeahaight said:
How much ice at a temperature of 10°C
Did you miss a minus sign there?

Yeahaight and etotheipi
jbriggs444 said:
Did you miss a minus sign there?
Yes, I did, sorry.

So solve the problem in steps. Heat the ice until it is at melting temperature. Melt the ice. Then heat the resulting water until it is at the final temperature.

Yeahaight
jbriggs444 said:
So solve the problem in steps. Heat the ice until it is at melting temperature. Melt the ice. Then heat the resulting water until it is at the final temperature.
Well, how do I do that if the mass of the ice isn't given?

Yeahaight said:
Well, how do I do that if the mass of the ice isn't given?

That's what you're trying to find. Call it ##m## and come up with an algebraic expression!

Yeahaight and jbriggs444
jbriggs444 said:
So solve the problem in steps. Heat the ice until it is at melting temperature. Melt the ice. Then heat the resulting water until it is at the final temperature.
So, the formula would be m=m1+m2?

Yeahaight said:
So, the formula would be m=m1+m2?

I'm not quite sure what that means. How much heat is required to heat a mass ##m## of ice from ##-10## degrees to ##0## degrees? How much heat is required to melt a mass ##m## of ice? How much heat is required to heat a mass ##m## of ice from ##0## degrees to ##20## degrees? What is the total amount of heat required, in terms of ##m##?

Yeahaight
etotheipi said:
I'm not quite sure what that means. How much heat is required to heat a mass ##m## of ice from ##-10## degrees to ##0## degrees? How much heat is required to melt a mass ##m## of ice? How much heat is required to heat a mass ##m## of ice from ##0## degrees to ##20## degrees? What is the total amount of heat required, in terms of ##m##?
So, basicly my plan was -
Find the total amount of mass by changing the formulas up a bit, because every heat formula has a m in it. So I thought about changing the formulas so I find the m because I already have the other values given.
I thought about doing every step jbriggs said but changing the formulas required for the step, so I find the mass not the heat, because the heat is already given and when I do that, I just count up every mass - m1, m2

For now, treat the 3 stages separately. In the relevant equations section you included ##Q = mc\Delta T##. With that in mind, how much heat (##Q##) is required to raise a mass ##m## of ice, with ##c = c_{ice}##, by ##10## degrees?

Can you do the same for the heating of water from ##0## degrees to ##20## degrees?

Last edited by a moderator:
Yeahaight
Suppose you had 1 kg of ice. How much heat would it take to first raise its temperature to 0 C, then melt it, and then raise the temperature of the resulting water to 20 C?

Lnewqban and Yeahaight
Chestermiller said:
Suppose you had 1 kg of ice. How much heat would it take to first raise its temperature to 0 C, then melt it, and then raise the temperature of the resulting water to 20 C?
When I have done that, how do I calculate the mass?

Yeahaight said:
So, the formula would be m=m1+m2?
Are you not seeing that the all of the ice turns into water and the mass does not change? There is only one m.

hutchphd said:
Are you not seeing that the all of the ice turns into water and the mass does not change? There is only one m.
Yeah, I figured that out already. The problem right now is how do I calculate the mass, if I know the total amount of heat.

Yeahaight said:
Yeah, I figured that out already. The problem right now is how do I calculate the mass, if I know the total amount of heat.
@Chestermiller gave you all you need.

You can figure how much heat to deal with 1 kg.
You know how much heat you have.
So how many kg can you deal with, given that much heat?

Yeahaight
Yeahaight said:
When I have done that, how do I calculate the mass?
You got to be kidding. If you have $1.00 dollar, and each item costs 20 cents ($0.20), how many items can you buy?

Last edited:

## 1. What is the formula for calculating the amount of heat?

The formula for calculating the amount of heat is Q = mcΔT, where Q is the amount of heat, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

## 2. How do you convert kJ to J?

To convert from kJ to J, you simply multiply the value in kJ by 1000. In this case, 80 kJ would be equivalent to 80,000 J.

## 3. How much ice can be melted with 80 kJ of heat?

The amount of ice that can be melted with 80 kJ of heat depends on the mass of the ice and its initial temperature. Using the formula Q = mcΔT, you can calculate the mass of ice that can be melted by rearranging the formula to m = Q / cΔT.

## 4. What is the specific heat capacity of ice?

The specific heat capacity of ice is 2.108 J/g°C. This means that it takes 2.108 joules of heat to raise the temperature of 1 gram of ice by 1 degree Celsius.

## 5. How does the specific heat capacity of ice affect the amount of ice that can be melted?

The higher the specific heat capacity of a substance, the more heat is required to raise its temperature. Therefore, the high specific heat capacity of ice means that it requires a significant amount of heat to melt, so 80 kJ may not be enough to melt a large amount of ice.

Replies
3
Views
1K
Replies
17
Views
3K
Replies
11
Views
1K
Replies
4
Views
1K
Replies
10
Views
2K
Replies
8
Views
2K
Replies
6
Views
3K
Replies
3
Views
2K
Replies
4
Views
6K
Replies
1
Views
1K