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

[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?

 

[jbriggs444]

How much ice at a temperature of 10°C

Did you miss a minus sign there?

 

[Yeahaight]

Did you miss a minus sign there?

Yes, I did, sorry.

 

[jbriggs444]

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]

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?

 

[etotheipi]

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]

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?

 

[etotheipi]

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]

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, basically 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

 

[etotheipi]

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?

 

[Chestermiller]

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?

 

[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?

When I have done that, how do I calculate the mass?

 

[hutchphd]

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.

 

[Yeahaight]

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.

 

[jbriggs444]

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?

 

[Chestermiller]

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?