How to find internal energy with constant temperature?

In summary, there is some discrepancy in how heat is defined, with some sources stating it as thermal energy transferred between systems and others defining it as energy stored within a system. The heat formula, Q=mc(T2-T1), is an approximation as it assumes a constant specific heat even though it changes with temperature. This raises the question of whether there is a single equation that accurately calculates the internal energy of a system with no temperature change.
  • #1
EastWindBreaks
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since specific heat c changes with temperature, but its treated as a constant in the heat formula, so that means that heat formula Q=mc(T2-T1) is just an approximation? correct?

I see some texts define heat as Heat, q, is thermal energy transferred from a hotter system to a cooler system that are in contact.(from Khan Academy), and some texts define it as energy stored inside of something. from the heat formula, if there is no temperature change, then the heat is 0. So the second definition is incorrect?

do we have a single equation that calculates internal energy stored in a system with no temperature change, for example at a given instant of a bottle of water?
 
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I just realized that I should post this in the homework section, I can't find the delete button for this post.
 

1. How is internal energy defined?

Internal energy is the total energy contained within a system, including the kinetic and potential energies of all the particles within the system.

2. What is the formula for calculating internal energy with constant temperature?

The formula for calculating internal energy (U) with constant temperature (T) is U = n * Cv * T, where n is the number of moles of gas and Cv is the molar specific heat at constant volume.

3. How does the concept of constant temperature affect internal energy?

When temperature is constant, the internal energy of a system remains constant as well. This means that any changes in the system's internal energy must come from work or heat being added or removed from the system.

4. Why is it important to consider constant temperature when calculating internal energy?

Constant temperature is important to consider because it allows us to isolate the change in internal energy caused by work or heat, rather than changes in temperature. This is important in understanding the behavior of a system and its energy transformations.

5. Can internal energy change while temperature remains constant?

Yes, internal energy can change while temperature remains constant. This is because internal energy is affected by factors other than temperature, such as changes in pressure or volume. As long as the temperature remains constant, the change in internal energy will be equal to the work or heat added or removed from the system.

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