Thermodynamics question

In summary: Maybe, but there are at least two other reasonable interpretations. There is still useful heat available in condensate at 100C, so could take everyting as finishing at 60C. Better still, the initial condensate is useful down to almost 30C, so the minimum vapor required is less again.Maybe, but there are at least two other reasonable interpretations. There is still useful heat available in condensate at 100C, so could take everyting as finishing at 60C. Better still, the initial condensate is useful down to almost 30C, so the minimum vapor required is less again.
  • #1
AlexPilk
26
0

Homework Statement


There are 2 kg of water in an aluminium pot at the temperature of 30C. What is the mass of water vapor (100C) needed to heat the pot with water to 60C? Mass of the pot = 0.5kg

m(water)=2kg
m(pot)=0.5kg
T1=30C
T2=60C
c(water)=4200 J/kg*C
c(aluminium)=890 J/kg*C
T(water vapor)=100*C
c(water vapor)= 2020 J/kg*C
m(water vapor)=?

2. The attempt at a solution

Q=Q1+Q2
Q=c(water)*m(water)*(T2-T1)+c(aluminium)*m(aluminium)*(T2-T1)

I supposed that
Q=c(vapor)*m(vapor)*(T2-T(vapor))
But then Q would be less than 0 since the temperature difference is less than 0. What is the right way to write this last equation? And the final equation to find the mass of water vapor?
Thank you!
 
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  • #2
You write Q=c(vapor)*m(vapor)*(T2-T(vapor)), but the formulation says What is the mass of water vapor (100 C), not taking account of the condensation of vapor water. This is, we use m Kg of vapor water to heat up the Al pot, which transfer heat to the water inside it. I'm thinking more of Q=c(vapor)*m(vapor)*(100)

On the other hand, you are supposing that both Al pot and the water inside it will reach the same temperature (T2). That would be the case according to zeroth law of thermodynamics, in thermal equilibrium (for large t, time). One could put it like: 1) Final T2 in the pot for the water to reach 60c? and 2) mass of vapor water to heat the pot to that T2 calculated in 1. This is my guess...
 
  • #3
At best, this is a poorly (imprecisely) worded problem. I think what they are asking is how much water vapor has to condense from vapor to liquid water at 100 C to supply the heat required to heat up the pot and its contents to 60C. So, how much heat does it take to heat up the contents?

Chet
 
  • #4
Chestermiller said:
At best, this is a poorly (imprecisely) worded problem. I think what they are asking is how much water vapor has to condense from vapor to liquid water at 100 C to supply the heat required to heat up the pot and its contents to 60C. So, how much heat does it take to heat up the contents?

Chet
Maybe, but there are at least two other reasonable interpretations. There is still useful heat available in condensate at 100C, so could take everyting as finishing at 60C. Better still, the initial condensate is useful down to almost 30C, so the minimum vapor required is less again.
 
  • #5
haruspex said:
Maybe, but there are at least two other reasonable interpretations. There is still useful heat available in condensate at 100C, so could take everyting as finishing at 60C. Better still, the initial condensate is useful down to almost 30C, so the minimum vapor required is less again.
Yes. I too thought about the possibility of taking the condensate down to 60, and this is certainly also a valid interpretation. As far as taking the condensate all the way down to 30, it doesn't seem like this can be done because of 2nd law constraints. Can you think of a way?

Chet
 

1. What is thermodynamics?

Thermodynamics is a branch of physics that deals with the study of heat and its relationship to other forms of energy, such as work. It also includes the study of how energy is transferred between different systems and how it affects the properties of matter.

2. What are the laws of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law states that the total entropy (disorder) of a closed system will always increase over time. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.

3. How is thermodynamics used in everyday life?

Thermodynamics is used in many areas of everyday life, including heating and cooling systems, power generation, refrigeration, and cooking. It also plays a role in understanding weather patterns and climate change.

4. What is the difference between heat and temperature in thermodynamics?

Heat is a form of energy that is transferred from one system to another due to a temperature difference. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a system. In other words, heat is the energy being transferred, while temperature is a measure of the intensity of that energy.

5. Why is thermodynamics important in the study of chemistry?

Thermodynamics is important in the study of chemistry because it helps us understand the energy changes that occur during chemical reactions. It also allows us to predict the direction of a chemical reaction and determine the conditions under which it will occur spontaneously. This information is crucial in fields such as chemical engineering and materials science.

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