# Is there a clear analogy here between volume and entropy? Looking at: (dQ)/T=dS, (dW)/P=dV

Is there a clear analogy here between volume and entropy? Looking at: $\frac{dQ}{T}=dS,\frac{dW}{P}=dV$
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minotaurafe
The general expression for the first law (using the OP sign convention) is: $dE=\delta q+\delta w$. When the process is reversible it is possible to write: $dE=TdS+PdV$. This expression is the diferential of a function E(S,V):
$dE=\frac{\mathrm{\partial }E}{\mathrm{\partial }S}dS+\frac{\mathrm{\partial }E}{\mathrm{\partial }V}dV$
The similarity between V and S in the expression is that both are independent functions of the internal energy, while temperature and pressure are partial derivatives:
$T=\frac{\mathrm{\partial }E}{\mathrm{\partial }S}$
$P=\frac{\mathrm{\partial }E}{\mathrm{\partial }V}$