Specific heat, latent heat, and temp

In summary, the system starts at a temperature of 21.0 Celsius and is placed in a freezer where energy is removed at a constant rate. The water takes 10 minutes (or 600 seconds) to cool to 0 Celsius and freeze into ice. After this, the ice continues to cool and after one hour, the temperature reaches T_B, which is off the scale on the given figure. The latent heat of fusion for this process is 333.7J/g. In order to find the temperature after one hour, the mass of the system and specific heats of water and ice are needed. The temperatures at various points during the process can be found using the equations ms(T_A)/t1 = mL/(t2-t
  • #1
jaded18
150
0
The system, originally at T_A = 21.0 Celsius, is placed in a freezer, where energy is removed from it in the form of heat at a constant rate. The figure shows how the temperature of the system takes t_1 = 10 min = 600 s to drop to 0 Celsius, after which the water freezes. Once the freezing is complete, the temperature of the resulting ice continues to drop, reaching temperature T_B after an hour.

http://session.masteringphysics.com/problemAsset/1013967/12/1013967B.jpg

If the cooling power remains constant, what will be the temperature of the system T_B after it has been in the freezer for exactly 1 hour? This temperature is off scale on the figure.

also: latent heat of fusion (ice to water phase change at 0 Celsius) = 333.7J/g
____________________

I know that after the water cools to 0 Celsius and freezes, the time that remains before the one hour mark is 722 sec and that the constant cooling power is 36.6J/s which I got by determining how much energy that has to be transferred out of the system as heat Q to lower its temperature to 0 =(2.20*10^4) and dividing it by 600s.

So... that means that in addition to 2.20*10^4 J that was required to bring the T from 21 to 0, we have to consider the energy for phase change (Q=mL=250(333.7)) and also the energy that I calculated to be 26425.2 J in the very beginning with the cooling power and time.

I feel like I'm going around in circles. Help?
 
Physics news on Phys.org
  • #2
I have just one confusion. You have to find the temp of the whole thing after two hours from the start at 21 C?
 
  • #3
no, I thought I said ONE hour...
 
  • #4
(You mentioned “system T_B after it has been in the freezer for exactly 1 hour?” Hence the confusion.)

You cannot get the absolute value of heat transfer rate because you haven’t specified the mass.

Take the mass to be m, sp heat of water to be s, sp heat of ice to be s2, time for water to cool to zero t1; time for water to freeze is t2 –t1, and time for ice to cool to T_B be t3. Initial temp of water is T_A=21 C, final temp of ice is (-T_B). L is the latent heat of fusion.

If the rate of heat taken away is constant, then,

ms(T_A)/t1 = mL/(t2-t1) = ms2*(T_B)/(t3-t2)

m cancels out. s2 is reqd. t2 can be found from the 1st two eqns.
 

1. What is specific heat and how is it measured?

Specific heat is the amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius. It is typically measured in joules per gram per degree Celsius (J/g°C) or calories per gram per degree Celsius (cal/g°C).

2. How does specific heat differ between different substances?

The specific heat of a substance depends on its chemical composition and physical properties. For example, water has a high specific heat due to its strong hydrogen bonding, while metals have lower specific heats due to their metallic bonding.

3. What is latent heat and how is it different from specific heat?

Latent heat is the amount of heat required to change the phase of a substance without changing its temperature. It is different from specific heat, which only applies to changes in temperature. Latent heat is also typically higher than specific heat.

4. How does temperature affect specific heat and latent heat?

As temperature increases, the specific heat of a substance typically decreases. This is because the substance's molecules have more kinetic energy and therefore require less heat to raise their temperature. On the other hand, latent heat remains constant regardless of temperature.

5. What are some real-life applications of specific heat, latent heat, and temperature?

Specific heat, latent heat, and temperature are important concepts in fields such as thermodynamics, chemistry, and meteorology. They are used to understand and predict changes in temperature, as well as to design and improve various technologies, such as refrigerators, air conditioners, and power plants.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
908
  • Introductory Physics Homework Help
Replies
1
Views
924
  • Introductory Physics Homework Help
Replies
1
Views
573
  • Introductory Physics Homework Help
Replies
4
Views
968
  • Introductory Physics Homework Help
Replies
2
Views
789
  • Introductory Physics Homework Help
Replies
15
Views
794
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
8K
Back
Top