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In this lecture, we explore thermodynamic potentials and Maxwell's relations. The first law for a homogeneous system of a pure substance undergoing a reversible process can be expressed as du = dq - pdv. By replacing dq with tds from the second law, we get du = tds - pdv, showing the dependence of internal energy on entropy and volume. This demonstrates that the homogeneous system has two degrees of freedom: mechanical and thermal. The variables entropy and volume are independent and extensive in this context.
