Measuring Heat Capacity: Solving for Heat Transfer in Thermal Contact

In summary, to measure the heat capacity of an object, you can use the equation C = Q/delta T, where C is the heat capacity, Q is the heat gained or lost, and delta T is the change in temperature. In this specific example, the heat capacity of a chunk of metal is calculated by using the heat gained by the water and the change in temperature of the metal. This can also be used to find the specific heat capacity of the metal by dividing the heat capacity by the mass of the metal.
  • #1
jlmac2001
75
0
Here's the problem:

To measure the heat capacity of an object, all you usually have to do is put it in thermal contact wit another object whose heat capacity you know. As an example, suppose that a chuck of metais immersed in boiling water (100 degrees), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20 degrees Celcius. After a minute of so, the temperature of the contents of the cup is 24 degrees celcius. Assume during this time n significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible.

(a) How much heat gained by the water?

For this one, would I use C = Q/delta T and solve for Q? If so, what is C?

(b) How much heat is lost by the metal?

Not sure about this one? Don't know how to start this one.

(c)What is the heat capacity of this chunk of metal?

Would I use the same eqn. that I used in part a?

(d)If the mass of the chunk of metal is 100g, what is its specific heat capacity?

I think I would use c=C/m. But what is C?
 
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  • #2
(a) How much heat gained by the water?

For this one, would I use C = Q/delta T and solve for Q? If so, what is C?
Yes, assuming that "delta T" is "change in T" (I had first thought of T as time!) delta Q= C* delta T (Notice that I am saying "delta Q" rather than Q). Notice that the problem said "put it in thermal contact with another object whose heat capacity you know". What is the heat capacity of water? The water has increased temperature from 20 to 24 degrees: it's heat content has increased by 4 times the heat capacity of water.

(b) How much heat is lost by the metal?
Where did any heat lost by the metal go? You are told to " Assume during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible." Any heat lost by the metal is gained by the water. This answer should be exactly the same as the answer to (a).

(c)What is the heat capacity of this chunk of metal?

Would I use the same eqn. that I used in part a?
Yes. The metal has decreased tempeature from 100 degrees to 24 degrees so delta T is 76. Now that you know delta Q (from (a) or (b)) and delta T, you can solve for C.

(d)If the mass of the chunk of metal is 100g, what is its specific heat capacity?

I think I would use c=C/m. But what is C?
It is the heat capacity you just calculated in (c), of course!
 
  • #3
c is specific heat, which is equal to ΔQ/mΔT.

C is heat capacity, is equal to ΔQ/ΔT.
 

1. What is heat capacity and why is it important?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. It is an important concept in thermodynamics as it helps us understand how materials respond to changes in temperature and how much heat is needed to achieve a desired temperature change.

2. How is heat capacity measured?

Heat capacity can be measured using various techniques, such as calorimetry, differential scanning calorimetry, and specific heat capacity measurements. These methods involve controlling the temperature of a substance and measuring the amount of heat needed to achieve a certain temperature change.

3. What factors affect the heat capacity of a substance?

The heat capacity of a substance is affected by its mass, its chemical composition, and its physical state. For example, substances with higher molecular weights tend to have higher heat capacities, and solids generally have higher heat capacities than liquids or gases.

4. How can heat transfer be solved for in thermal contact?

In thermal contact, heat transfer can be solved for using the equation Q=mcΔT, where Q is the amount of heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. This equation can be used to calculate the amount of heat needed to achieve a desired temperature change or the change in temperature resulting from a known amount of heat transfer.

5. How can heat capacity be used in practical applications?

Heat capacity is an important concept in various fields, including engineering, chemistry, and meteorology. It is used to design and improve heating and cooling systems, understand the behavior of materials in different environments, and predict and analyze weather patterns. It is also essential in the development of new materials and technologies that require precise temperature control.

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