First take the case where the heat is lost from a constant volume system Then dQv can be identified with dU if there is no non-pV work involved. Putting this into eq gives dS-dUT全0.0r0全dU-TdS du<TdS (const. V, no non-pV work) When the heat is lost from the system under conditions of constant pressure and when no non )V ork is involved 4上一内容下一内容◇回主目录 返回 2021/2/21
上一内容 下一内容 回主目录 返回 2021/2/21 First take the case where the heat is lost from a constant volume system. Then dQv can be identified with dU if there is no non-pV work involved. Putting this into eq.gives dS - dU/T ≧0, or 0 ≧ dU- T dS dU≤TdS (const. V, no non-pV work) When the heat is lost from the system under conditions of constant pressure and when no nonpV work is involved
the only modification is to identify dQp with dh, the change of enthalpy of the system Then ds-dH/T≡0.or0≡dH-TdS dhs tds (const. p, no non-pV work) These expressions can be simplified even more by introducing two new thermodynamic functions They are defined as follows Helmholtz function: A=U-TS Gibbs function G=H-TS 4上一内容下一内容◇回主目录 返回 2021/2/21
上一内容 下一内容 回主目录 返回 2021/2/21 the only modification is to identify dQp with dH, the change of enthalpy of the system. Then dS – dH /T ≧ 0, or 0 ≧ dH - T dS dH≤ TdS (const. p, no non-pV work) These expressions can be simplified even more by introducing two new thermodynamic functions. They are defined as follows: Helmholtz function: A = U – T S Gibbs function: G = H – T S
How G and a simplify the expressions Consider what happens to them when the state of a system changes at constant temperature da=dU -Tds(const. t) dG=dH-Tas(const T) Now introduce Tas>du (const. V) Tds>dH(const. P) daso (const. T,V, no non-pV work) dG<o (const T, P, no non-pV work) 4上一内容下一内容令回主目录 返回 2021/2/21
上一内容 下一内容 回主目录 返回 2021/2/21 How G and A simplify the expressions Consider what happens to them when the state of a system changes at constant temperature: dA = dU –TdS (const.T) dG = dH – TdS (const.T) Now introduce TdS≥dU (const. V) TdS≥dH (const. P) dA≤0 (const. T,V,no non-pV work) dG≤0 (const. T,P,no non-pV work)
These inequalities are the most important conclusions from thermodynamics in chemistry. Some remarks on the helmholtz function When the changes in a system are constrained to occur under conditions of constant temperature and volume eq above determines whether they can occur spontaneousl 4上一内容下一内容◇回主目录 返回 2021/2/21
上一内容 下一内容 回主目录 返回 2021/2/21 These inequalities are the most important conclusions from thermodynamics in chemistry. Some remarks on the Helmholtz function. When the changes in a system are constrained to occur under conditions of constant temperature and volume eq. above determines whether they can occur spontaneously
A change corresponding to a decrease in a can occur spontaneously Systems tend to move naturally towards states of lower A and the criterion of equilibrium is(dATV=. (n,W=0) We shall now demonstrate the connection between △ A and w max 4上一内容下一内容◇回主目录 返回 2021/2/21
上一内容 下一内容 回主目录 返回 2021/2/21 A change corresponding to a decrease in A can occur spontaneously. Systems tend to move naturally towards states of lower A,and the criterion of equilibrium is (dA)T,V =0. ( n,W`=0) We shall now demonstrate the connection between △A and Wmax