Internal energy equals to average kinectic energy ?

In summary, for an ideal gas, the molar heat capacity, Cv, is equal to 3R/2 only for ideal monatomic gases. Additionally, using this value for Cv, the integral of nCv dT from initial temperature, Ti, to final temperature, Tf, can be simplified to (3/2)NkΔT, where N is the number of particles and k is the Boltzmann constant.
  • #1
Outrageous
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For ideal gas , can I assume Cv dT = nkT (3/2)
, thank you
 
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  • #2
Outrageous said:
For ideal gas , can I assume Cv dT = nkT (3/2)
, thank you
No. Molar heat capacity, Cv = 3R/2 only for ideal monatomic gases. You are also mixing temperature change with temperature here.

Using molar heat capacity 3R/2 for a monatomic ideal gas:

[itex]\int_{Ti}^{Tf} nC_vdT = \frac{3}{2}nR(T_f - T_i) = \frac{3}{2}nR\Delta T = \frac{3}{2}Nk\Delta T[/itex]
AM
 
  • #3
Andrew Mason said:
No. Molar heat capacity, Cv = 3R/2 only for ideal monatomic gases. You are also mixing temperature change with temperature here.

Using molar heat capacity 3R/2 for a monatomic ideal gas:

[itex]\int_{Ti}^{Tf} nC_vdT = \frac{3}{2}nR(T_f - T_i) = \frac{3}{2}nR\Delta T = \frac{3}{2}Nk\Delta T[/itex]



AM

Thanks for compact explanation.
 

1. What is internal energy?

Internal energy is the total energy contained within a system, including both kinetic and potential energy.

2. What is average kinetic energy?

Average kinetic energy is the average amount of energy possessed by particles in a system due to their motion.

3. How is internal energy related to average kinetic energy?

According to the kinetic theory of gases, the internal energy of a system is equal to the sum of the average kinetic energies of all the particles in the system.

4. Why is it important to understand the relationship between internal energy and average kinetic energy?

Understanding this relationship can help scientists and engineers better understand and predict the behavior of systems, such as gases, and how they respond to changes in temperature and pressure.

5. How can we calculate the internal energy and average kinetic energy of a system?

The internal energy of a system can be calculated using the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system. Average kinetic energy can be calculated using the kinetic energy equation, which is 1/2 * mass * velocity^2.

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