Thermodynamics Problem: Calculating Mass of Lead and Water in Equilibrium

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Discussion Overview

The discussion revolves around a thermodynamics problem involving the calculation of the mass of lead and water remaining in an insulated bucket after reaching thermal equilibrium. The scenario includes the phase transitions of both lead and water, with participants exploring the implications of these transitions on the final mass calculations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents an initial calculation using specific heat capacities for lead and water, but expresses uncertainty about the final answer and the role of steam production.
  • Another participant questions the behavior of water at 100°C, hinting at boiling and phase changes.
  • A participant points out a potential error in the heat equation, suggesting that the mass of water should be used instead of lead in the calculations.
  • One participant proposes that not all water boils away and asks for the final temperature of the system under this assumption.
  • Another participant emphasizes the need to consider the phase transition of lead from liquid to solid, as well as the vaporization of some water.
  • A humorous remark is made about the idea of lead changing to water, referencing alchemy, while questioning the definitions of water and steam in the context of mass calculations.
  • One participant clarifies that the mass of lead remains constant at 1.25 kg, suggesting that the problem could have been framed to ask for the proportion of water to steam instead.
  • There is a reiteration of the importance of phase transitions in determining the final mass and temperature of the system.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the calculations and assumptions about phase changes, with no consensus reached on the final mass or the interpretation of steam in relation to the problem.

Contextual Notes

Participants highlight the need to consider phase transitions and the definitions of water and steam, indicating that assumptions about these factors significantly affect the calculations. The discussion remains unresolved regarding the exact final mass of the materials.

chipM
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Homework Statement



Not sure if this is the right thread for this question but here goes :

A worker pours 1.25 kg of molten lead at a temperature of 327.3 into 0.500 kg of water at a temperature of 75 C in an insulated bucket of negligible mass. Assuming no heat loss of the surroundings. Calculate the mass of lead and water remaining in the bucket when the materials have reached thermal equilibrium.

Homework Equations





The Attempt at a Solution



C(water)=4190
C(lead ) = 130

Q=mcdelta T

(1.250)(130)(600.3-t)= Q (lead)

(1.250)(4.19)(T-348)=Q(water)

expand rearrange :

97500-162.5T=5237.5T-1822650

T= 355.57333

i kind of lost here , that's all i have done

the answear is

(1.743kg) - remember, steam will be produced!

but how is this the answear can someone show me the working ?

thanks
 
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What happens to water when it reaches a temperature of 100 C? Hint: think teapot.
 
SteamKing said:
What happens to water when it reaches a temperature of 100 C? Hint: think teapot.

boiling point of water ? .

but how is the mass achieved ?
 
You have used the mass of lead (1.25 kg) instead of the mass of water (0.500 kg) in writing the equation for the amount of heat received by the water.
 
Start out by assuming that not all the water boils away, but that there is enough heat in the lead to raise the temperature of the water to its boiling point. Under these circumstances, what is the final temperature of the lead and water?
 
Take into consideration that the melting point of lead is 600 K (327.3oC) so the lead must go a phase transition to solid
 
Lead changing to water or vice-versa? Alchemy perhaps?
If all that's left is lead and water then steam must count as water ...

Or maybe lead oxidizes or ... ?
 
The problem states "molten lead at 327.3 oC"

My textbook has the melting point of lead to be 600.3 K. A phase transition (liquid to solid) for the lead is necessary, as well as phase transition from liquid to vapor for some of the water.

From where are you coming with an alchemy reference?

The quoted "answer" is obtained when the phase transitions are taken into consideration.
 
PHd Austin said:
The problem states "molten lead at 327.3 oC"

My textbook has the melting point of lead to be 600.3 K. A phase transition (liquid to solid) for the lead is necessary, as well as phase transition from liquid to vapor for some of the water.

From where are you coming with an alchemy reference?

The quoted "answer" is obtained when the phase transitions are taken into consideration.

The mass of lead obviously doesn't change, so 50% of the answer is a no-brainer if there ever was one. It starts and ends at 1.25 kg. Easy, huh?

If we decide not to call steam "water" then obviously one can ask for the proportion of water to steam. The problem should have been stated as "what is the remaining proportion of water to vapor".

Alchemy is the changing of one element to another, which would have to happen if the mass of lead were to chage - unless, as I said, we consider chemical reactions like oxidation.
 

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