# So I was doing problem and used formula Eq.1 to find Energy in isochoric process. ΔE=3/2pV and get a bad result so now i saw the correct formula: ΔE=nc_vΔT What is doing on? can somebody link consistent source of that formulas etc.?

Emmanuel Pace 2022-07-22 Answered
So I was doing problem and used formula Eq.1 to find Energy in isochoric process.
$\mathrm{\Delta }E=\frac{3}{2}pV$
and get a bad result so now i saw the correct formula:
$\mathrm{\Delta }E=n{c}_{v}\mathrm{\Delta }T$
What is doing on? can somebody link consistent source of that formulas etc.?
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## Answers (1)

repotasonwf
Answered 2022-07-23 Author has 12 answers
The problem is the two equations for an ideal (perfect) gas should be
$E=\frac{3}{2}pV$
and
$E=n{C}_{v}T$
Where the first equation can be derived from the second.
For an ideal gas, any process, internal energy is a function of temperature only according to the following where ${C}_{v}$ is condidered independent of temperature
$E=n{C}_{v}T$
Although we normally deal with changes in internal energy and changes in temperature, this equation is based on assigning a value of zero to internal energy at absolute zero temperature.
Next, for an ideal gas we have
${C}_{v}=\frac{3}{2}R$
Next, for an ideal gas we have
${C}_{v}=\frac{3}{2}R$
Substituting into the equation for internal energy, we get
$E=\frac{3}{2}nRT$
From the ideal gas equation we have
$pV=nRT$
Finally, substituting this into the previous equation we get
$E=\frac{3}{2}pV$
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