Specific heat capacity varies with temperature.

In summary, the task is to find the change in energy (E) for heating a .8 kg disk of iron from 20 C to 400 C, given that the specific heat capacity changes from 456 at 20 C to 615 at 400 C. This can be solved by using the equation E = mC(dT) and integrating both sides of the equation after applying the product rule. Another approach could be plotting the specific heat capacity against kelvin and using the specific heat capacity at the midpoint (483.15k) to find the solution.
  • #1
necromanzer52
12
0

Homework Statement


Heating a .8 kg disk of iron from 20 C to 400 C, but the specific heat capacity changes from 456 at 20 C, to 615 at 400 C. It hints that I'm supposed to find the average to solve the equation.


Homework Equations


E = mC(dT)


The Attempt at a Solution


I have a strong feeling, that I'm supposed to use calculus to solve this, but I can't think of any equations to differentiate, or how it would be, in any way, useful.

I've also thought about plotting the specific heat capacity against kelvin, and using the specific heat capacity at the midpoint (483.15k)
 
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  • #2
Just a hint

dE = m d(CT)
dE = m (CdT + TdC) (product rule)

Integrate both sides and find the answer.
 

1. What is specific heat capacity?

Specific heat capacity is the amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius. It is measured in joules per gram per degree Celsius (J/g°C).

2. How is specific heat capacity related to temperature?

Specific heat capacity varies with temperature, meaning that the amount of heat energy needed to change the temperature of a substance by 1 degree Celsius will change as the temperature changes. This is due to the changes in the internal energy and molecular motion of the substance at different temperatures.

3. Why does specific heat capacity vary with temperature?

The varying specific heat capacity is due to the fact that as the temperature of a substance increases, the internal energy and molecular motion also increase. This results in a greater amount of heat energy needed to produce the same change in temperature.

4. How is specific heat capacity measured?

Specific heat capacity can be measured experimentally by using a calorimeter. The substance is heated to a known temperature and then placed in a container of water with a known volume and temperature. The change in temperature of the water is then measured, and using the equation Q = mcΔT, the specific heat capacity can be calculated.

5. How does specific heat capacity affect everyday life?

Specific heat capacity plays a role in many everyday activities, such as cooking, heating and cooling systems, and even the weather. It determines how quickly a substance will heat up or cool down, and can also affect the amount of energy needed to maintain a certain temperature. For example, substances with high specific heat capacity, like water, are able to retain heat for longer periods of time, making them useful for heating and cooling purposes.

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