In a constant pressure process, the change in internal energy is U=3/2nRT=3/2P(V_2-V_1) However in a constant volume, is the change in internal energy U=3/2nRT=V(P_2−P_1) ?

Jorge Schmitt

Jorge Schmitt

Answered question

2022-11-06

In a constant pressure process, the change in internal energy is
U = 3 2 n R T = 3 2 P ( V 2 V 1 ) .
However in a constant volume, is the change in internal energy U = 3 2 n R T = V ( P 2 P 1 ) ?

Answer & Explanation

embutiridsl

embutiridsl

Beginner2022-11-07Added 26 answers

The thermodynamics of an ideal gas is entirely contained in two equations:
U = 3 2 n R T                                               [ 1 ] P V = n R T .                                               [ 2 ]
In a transformation (change of state) where pressure is kept fixed, equation [2] says that if the volume changes from V 1 to V 2 the temperature cannot remain fixed at the same value T. The change of volume must be accompanied by a change of temperature Δ T = P Δ V / n R
In a similar way, if volume is kept fixed, again from eq.[2] we can get the change of temperature corresponding to a change of pressure from P 1 to P 2
From the change of temperature, eq.[1] immediately provides the change of internal energy.

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