# Homework Help: Thermodynamics problem - need to find amount of water that boils

1. May 13, 2012

### sweetpete28

Thermodynamics problem -- need to find amount of water that boils

Suppose molten (liquid) lead, mass = 10.28 kg, is at its melting point. The lead is poured into water of mass = 658 g and initial temperature T = 18.7 degrees C. Find the amount of the water that boils. Assume no heat loss.

2. May 13, 2012

### rock.freak667

Re: Thermodynamics problem -- need to find amount of water that boils

Well the energy from the molten liquid will be the sum of the heat needed to cause the temperature of the water to rise to boiling point and the energy needed to change the phase of the water.

So you know that Q=mcΔT will be used for the energy needed to raise the temperature.

But what is the equation for the heat required to change the phase of the water? (what kind of 'heat' is it called?)

3. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Heat required to change the phase of the water is the Latent heat...right? Equation is Q = mL where L = 2260 kJ/kg. Right?

4. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Ok...um...how is this Wrong??

Heat loss by lead = (10.28)(130)(327.5-100) = 304031 J

Heat gain by water = (.658)(4186)(100-18.7) = 223931.7444 J

Mass of water turned to steam = Q / L = (304031 - 223931.7444) = 80099.25556 J = 80.09925556 kJ / 2260 kJ/Kg = .035 kg....please explain how this is wrong...thanks.

5. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

6. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Do I need to sue 2010 as specific heat of water?

7. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

8. May 13, 2012

### Staff: Mentor

Re: Thermodynamics problem -- need to find amount of water that boils

What's the heat of fusion of lead? What's the heat of vaporization of water? What's the specific heat of liquid water? You need to have all these constants on hand.

In what state does the lead begin? What energy is released when it turns from liquid to solid at its melting point?

9. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

ok....

Energy released when lead turns from liquid to solid at melting point:
(10.28 kg) x (25kJ/Kg) = 257kJ

Heat to raise water to 100 degrees Celsius:
(.658 kg) x (4186) x(100-18.7) = 223.9317kJ

Heat to change water to steam:
(.658) x (2260) = 1487.08kJ

Am I missing anything now?

10. May 13, 2012

### Staff: Mentor

Re: Thermodynamics problem -- need to find amount of water that boils

What temperature will the lead be at when it turns from liquid to solid? Suppose that only some of the water is boiled away. What will be the final temperature of everything that remains at the end?

11. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

100 degrees Celsius?

12. May 13, 2012

### Staff: Mentor

Re: Thermodynamics problem -- need to find amount of water that boils

13. May 13, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Both...but I guess that is not right. Final temp for everything that remains is 100?

14. May 14, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

What is the equation i need to set up?????

There is energy released when lead turns from liquid to solid, there is the heat needed to raise water to 100 degrees celsius, there is heat needed to change water to steam, there is heat lost by l;ead

15. May 14, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Do I need to use the specific heat of lead?

16. May 14, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Is the specific heat of lead needed to calculate the heat loss of the lead in addition to the energy released from the phase change (change from liquid to solid)?

17. May 14, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

Evidently not. One last chance to get this right...little help please on needed equation.

18. May 14, 2012

### Infinitum

Re: Thermodynamics problem -- need to find amount of water that boils

As for the question,

The heat released by lead = The heat required by water to reach 100 degrees + the heat required for it to vaporize.

Now, you dont know what the mass of water is, thats what you need to find out.

How did you get that mass to be 0.658 in that equation there then? That's the mass of lead...

19. May 14, 2012

### sweetpete28

Re: Thermodynamics problem -- need to find amount of water that boils

.658 Kg is the mass of the water; it's given in the problem.

Energy released when lead turns from liquid to solid = (10.28)(25kJ/Kg) = 257,000J

257000 + (10.28)(130)(327 - T) = (.658)(4186)(T - 18.7)

T = 182.2411368 degrees Celsius

Heat released by lead = 257000J + 193455.7448J = 450455.7448 J

Heat required by water to reach 100 degrees C = (.658)(4186)(100-18.7) = 223931.7444J

Q = Heat required by water to vaporize

450455.7448 = 223931.7444 + Q

Q = 226524.0004J = 226.524 kJ

m = 226.524 kJ / 2260kJ/Kg = .100 kg

So the answer is .100 Kg......yes? No?

20. May 14, 2012

### Infinitum

Re: Thermodynamics problem -- need to find amount of water that boils

Whoops, I inverted the masses.

And no, this isn't correct. The T you get is 182.25. Now if this were the final temperature of water, it would be waaay above boiling point, and no latent heat was considered.