Change of internal energy of an ideal gas

In summary, the internal energy of a system is the sum of its kinetic energy and potential energy. In an ideal gas, the internal energy is solely dependent on the temperature and is directly proportional to it. As the temperature increases, the internal energy also increases due to the increase in kinetic energy of the molecules. The internal energy remains unchanged if the gas undergoes a change in volume at constant temperature, but will change if both the volume and temperature change. The change in internal energy of an ideal gas can be calculated using the formula ΔU = nCvΔT, where ΔU is the change in internal energy, n is the number of moles of gas, Cv is the molar specific heat at constant volume, and Δ
  • #1
DevonZA
181
6

Homework Statement


upload_2017-5-16_9-52-57.png


Homework Equations


Δu = ∫ [(a-Ru)+bT+cT^2+dT^3]dT

The Attempt at a Solution



The answer of 6447kJ/kmol is given but I am struggling to get to this answer after integrating the above formula and inserting the given values.

Firstly would the integral of [(a-Ru)+bT+cT^2+dT^3]dT
be:

[(a-Ru)+bT^2/2+cT^3/3+dT^4/4] ?
 
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  • #2
No. The first term should be (a-Ru)T.
 
  • #3
mjc123 said:
No. The first term should be (a-Ru)T.

Is this because (a-Ru) is a constant?
eg. ∫1 dx = x
 
  • #4
Yes
 
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Likes DevonZA
  • #5
mjc123 said:
Yes

Thank you let me give that a try.
 
  • #6
upload_2017-5-16_11-12-38.png
 

Related to Change of internal energy of an ideal gas

1. What is the definition of internal energy?

The internal energy of a system is the sum of its kinetic energy and potential energy. It is a measure of the total energy contained within the system.

2. How is internal energy related to ideal gas?

In an ideal gas, the internal energy is solely dependent on the temperature of the gas. It is directly proportional to the temperature and is independent of the pressure and volume of the gas.

3. How does the internal energy of an ideal gas change with temperature?

As the temperature of an ideal gas increases, so does its internal energy. This is because the molecules in the gas gain more kinetic energy, increasing the overall energy of the system.

4. What happens to the internal energy of an ideal gas when it undergoes a change in volume?

If the gas undergoes a change in volume at constant temperature, the internal energy remains unchanged. However, if the gas undergoes a change in volume and temperature, the internal energy will change due to the change in kinetic energy of the molecules.

5. How can the change in internal energy of an ideal gas be calculated?

The change in internal energy of an ideal gas can be calculated using the formula ΔU = nCvΔT, where ΔU is the change in internal energy, n is the number of moles of gas, Cv is the molar specific heat at constant volume, and ΔT is the change in temperature.

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