Specific heat capacity, latent heat => ice water steam mixture

In summary, the final temperature of the container can be calculated by using the equation Q=mc(change in T) and Q=mL with the inputs of 100g of ice at 0°C, 50g of steam at 100°C, and 150g of water at 30°C. The sum of all Q changes must be zero, meaning that the energy of the steam contributes to the rise in temperature of the other items. Appropriate terms for heat of fusion and heat of vaporization must also be taken into account when calculating the final temperature.
  • #1
FelixISF
23
0

Homework Statement


A quantity of 100g of ice at 0°C and 50g steam at 100°C are added to a container that has 150g water at 30°C. What is the final temp of the container? Ignore the container itself in the calc.

Homework Equations


Q=mc (change in T)
Q=mL

The Attempt at a Solution


I know how to figure out this kind of problem with only 2 inputs, but with three i struggle with a good approach.
Can I just calculate the final temp for the water and the ice and then do the same for the resulting water temp and mass with the steam?
MOST IMPORTANTLY: what happens to the energy of the steam, when it becomes water? does it add to the system ?regards
 
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  • #2
With three inputs it is the same thing. Some items see their temperature drop some see their temperature rise, but (and this is very important) no heat leaves the system. Now Q is positive if the temperature of an item rises and negative if it decreases. Then you can say that the sum of all Q changes must be zero.

0 = m1c1ΔT1 + m2c2ΔT2+m3c3ΔT3

You can put together as many items as you want this way in one equation.

The energy of the steam stays in and contributes to the rise in the temperature of the other items. Of course you need to remember to add appropriate terms for the heat of fusion and heat of vaporization. You can write one equation taking everything into account.
 
  • #3


I would approach this problem by first identifying the known values and converting them to the appropriate units (e.g. grams to kilograms). Then, I would use the equations for specific heat capacity and latent heat to calculate the amount of energy required to change the temperature of the water and ice, as well as the amount of energy released when the steam condenses into water.

Next, I would use the principle of conservation of energy to determine the final temperature of the container. This principle states that the total energy of a closed system remains constant, so the amount of energy added to the system (from the ice and steam) must equal the amount of energy lost (through the resulting change in temperature).

In terms of the steam, its energy will be released as it condenses into water, adding to the total energy of the system. This energy will then be distributed among all the components in the container, resulting in a change in temperature.

To summarize, I would use a combination of equations and principles to determine the final temperature of the container, taking into account the specific heat capacity and latent heat of the different components.
 

1. What is specific heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

2. How is specific heat capacity measured?

Specific heat capacity is typically measured in units of joules per gram per degree Celsius (J/g°C) using a calorimeter.

3. What is latent heat?

Latent heat is the amount of heat absorbed or released by a substance during a phase change without a change in temperature.

4. How is latent heat involved in the ice-water-steam mixture?

In the ice-water-steam mixture, latent heat is involved in the phase changes between solid ice, liquid water, and gaseous steam. When heat is added, it is used to melt the ice or vaporize the water, rather than raising the temperature of the substance.

5. How does the specific heat capacity and latent heat differ between ice, water, and steam?

The specific heat capacity and latent heat of a substance depend on its phase. Ice has a lower specific heat capacity and latent heat compared to water and steam. Water has a higher specific heat capacity and latent heat than ice, but a lower specific heat capacity and latent heat than steam. Steam has the highest specific heat capacity and latent heat out of the three phases.

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