So I was doing problem and used formula Eq.1 to find Energy in isochoric process. Δ E = 3 2 p Vand get a bad result so now i saw the correct formula: Δ E = n c v Δ T What is doing on? can somebody link consistent source of that formulas etc.?

Question

So I was doing problem and used formula Eq.1 to find Energy in isochoric process.  Δ      E    =      3    2    p  Vand get a bad result so now i saw the correct formula:  Δ      E    =  n      c    v    Δ      T  What is doing on? can somebody link consistent source of that formulas etc.?

repotasonwf · Accepted Answer

The problem is the two equations for an ideal (perfect) gas should be  E  =      3    2    p  Vand  E  =  n      C          v        TWhere 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        TAlthough 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        =      3    2    RNext, for an ideal gas we have      C          v        =      3    2    RSubstituting into the equation for internal energy, we get  E  =      3    2    n  R  TFrom the ideal gas equation we have  p  V  =  n  R  TFinally, substituting this into the previous equation we get  E  =      3    2    p  V

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.?

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