# Problem of Thermodynamics

1. May 13, 2009

### ashvuck101

1. The problem statement, all variables and given/known data

An M gram chunk of hot iron is placed on a large piece of 0 ºC ice, causing m grams of ice to melt.

a. What will be the final temperature of the system?
b. What must have been the initial temperature of the hot iron?
c. What must have been the initial temperature of the hot iron?
d. Calculate part c) based on the following information M = 250g, m = 48g and the specific heat of iro in 0.44J / g ºC.

2. Relevant equations

q=mC(tf-ti)

3. The attempt at a solution

how am i ment to know what the final heat is without being given the heat of the iron all i know is it is above 0 ºC unless i am giving the answer as an equation?

am i missing something really obvious?

2. May 13, 2009

### redargon

Re: thermodynamics

I think they want answers in variable form (equation form) for a,b and c

3. May 13, 2009

### Andrew Mason

Re: thermodynamics

The final temperature is obvious. When the iron stops melting ice, what can you say about the flow of heat from the iron to the ice? What can you then say about the temperature difference between the iron and ice?

For some reason, b and c are the same question.

AM

4. May 26, 2009

### dgmatthews

Re: thermodynamics

I have exactly the same problem
is it possible to incorporate equation Q=mLf?

c1m1(Tf-Ti)=m2Lf

if so how would this be rearranged? would this be correct

Ti=((m2Lf)/(c1/m1))-Tf

so confused will appreciate any help at all

5. May 26, 2009

### redargon

Re: thermodynamics

what is Lf?

6. May 26, 2009

### fatra2

Re: thermodynamics

Hi there,

$$L_f$$ is the latente heat of ice.

The solution of this problem is quite simple. You must apply the energy consrvation law, and you find the answer. It takes heat/energy to transform 0°C ice into water ($$\Delta Q=mL_f$$), it takes heat to warm up the water ($$\Delta Q=c_{H_2O}m\Delta T$$), and this heat is taken from the hot iron mass ($$\Delta Q= c_{Fe}M\Delta T$$). You add all of that, and you find your answer.

Cheers

7. May 26, 2009

### dgmatthews

Re: thermodynamics

thank you, but im still a bit confused

i didnt incorporate $$\Delta Q=c_{H_2O}m\Delta T$$ because it dosnt say anything about the water changing temperature. only that it melts, so figure it was only a phase change. if the water only changes phase and remains at zero degrees does that not omit that part of the equation. the reason i say this is because the question suggests there is enough ice to absorb enough energy to bring the iron to zero degrees as well. is that right?

ok is this right?
$$\Delta Q= c_{Fe}M\Delta T=mL_f+c_{H_2O}m\Delta T$$

rearranged to find initial temp of iron
$$\Delta Q= T_{Fe i}=((ml_f+c_{H_2O}m\Delta T)/(c_{fe}m_{fe}))-T_{Fe f}$$

sorry bout the writing im not used to the coding but i hope u get what i mean.

8. May 26, 2009

### Andrew Mason

Re: thermodynamics

You are correct. The temperature of the water/ice does not change. Some of the ice just melts.
No. I don't think you mean that the two $\Delta T's$ are the same, but that is what you wrote. The first is the change in temperature of the iron and the second is the change in temperature of the water, which, as you have said, is zero.
The following is not correct:

$$\Delta Q= T_{Fe i}$$

Heat flow cannot be equated to temperature.

The following part is correct except for a missing minus sign, but you can simplify because that $\Delta T$ is zero:

$$T_{Fe i}=((ml_f+c_{H_2O}m\Delta T)/(c_{fe}m_{fe}))-T_{Fe f}$$

The heat flow equation has to contain the proper signs. Heat flow out is negative and heat flow in is positive. From the perspective of the iron:

$$Q_{iron} = - Q_{ice}$$

$$m_{iron}c_{iron}(T_f - T_i) = - m_{ice}L_f$$

AM

Last edited: May 26, 2009
9. May 26, 2009

### dgmatthews

Re: thermodynamics

thank u so much,
so after well cancel out n simplify is it safe to say

$$T_i = (- m_{ice}L_f)/(m_{iron}c_{iron})-T_f$$

n once again guys thankyou for all your help its hugely appreciated.

10. May 26, 2009

### dgmatthews

Re: thermodynamics

although this dosnt seem right when i plug in the given variables in part D
iron M = 250g, ice m = 48g and the specific heat of iro in 0.44J / g ºC.
given Lf ice= 334J/g

Ti iron = (-48x334)/(0.44x250)-0 = -145.7454545 ? that cant be right

11. May 26, 2009

### dgmatthews

Re: thermodynamics

ok i just realised a mistake
-Ti iron = (-5g x 334J)/(0.44J/g x 250g) = 15.18
does that sound right?

thanks

12. May 26, 2009

### Andrew Mason

Re: thermodynamics

Why is this not right? You melt 48 g. of ice requiring 334J/g for a total of 16,032 J. It takes 110 Joules to raise the temperature of the iron one degree C. (250 x .44) J/deg.

AM

13. May 29, 2009

### dgmatthews

Re: thermodynamics

yep sorry confused myself with another question that melts 5g of ice. thanks for all the help guys