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## Summary:

- A conflict conclusion was obtained in the 1st law of thermodynamics,

In thermodynamics, the internal energy (U) is the function of the volume (V) and temperature (T), U = U (T).

Therefore, according to the mathematics, dU = π dV + Cv dT, where π is internal pressure and Cv is the constant volume heat capacity.

Meanwhile, according to the 1st law, dU = δ w + δq, when under reversible process, dU = - p dV + C dT.

If we compare both, dU = π dV + Cv dT = - p dV + C dT. Since both V and T are free variables, we can get,

π = -p and Cv = C.

Obvious this is not right result. Based on Maxwell equation:

π = T (∂p/∂T)

Which part is wrong in my derivation?

Thanks in advance!

Therefore, according to the mathematics, dU = π dV + Cv dT, where π is internal pressure and Cv is the constant volume heat capacity.

Meanwhile, according to the 1st law, dU = δ w + δq, when under reversible process, dU = - p dV + C dT.

If we compare both, dU = π dV + Cv dT = - p dV + C dT. Since both V and T are free variables, we can get,

π = -p and Cv = C.

Obvious this is not right result. Based on Maxwell equation:

π = T (∂p/∂T)

_{V}-pWhich part is wrong in my derivation?

Thanks in advance!

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