Gas Laws and Processes PDF

Isometric Process PV – T relation Change in Enthalpy = 𝐶; if V = constant 𝑑ℎ 𝑷𝟏 𝑷𝟐 𝐶𝑝 = = 𝑑𝑡 𝑻...

Isometric Process PV – T relation Change in Enthalpy = 𝐶; if V = constant 𝑑ℎ 𝑷𝟏 𝑷𝟐 𝐶𝑝 = = 𝑑𝑡 𝑻𝟏 𝑻𝟐 ∆𝑯 = 𝒎𝑪𝒑∆𝑻 Change in Internal Energy Work Non – Flow 𝐶 = ; 𝑑𝑢 = 𝐶 𝑑𝑡 𝑊 = 𝑃𝑑𝑉 ; 𝑉 = 𝐶 ∆𝑼 = 𝒎𝑪𝒗 ∆𝑻 𝑾𝒏𝒇 = 𝟎 Isometric Process Work Steady – Flow Considering Ideal Gas Equation; 𝑃𝑣 = 𝑚𝑅𝑇 W = −𝛥𝑃𝐸 − ∆𝐾𝐸 − ∆𝑃𝑉 𝐖𝒔𝒇 = −𝒎𝑹∆𝑻 If 𝛥𝑃𝐸 & ∆𝐾𝐸 is neglected, therefore W = −𝑉 ∆𝑃 W =− vdP −𝑽 ∆𝑷 = − 𝒗𝒅𝑷  For non – flow system with paddle work (𝑊 ) considering figure, Isometric Process Change in Entropy 𝑄 𝑆= ∆𝑇 𝑑𝑄 𝑚𝐶𝑣𝑑𝑇 ∆𝑆 = = ∆𝑇 𝑇 ∆𝑆 = 𝑚𝐶𝑣𝑙𝑛 ; = 𝑄 + 𝑊 = 𝛥𝑈 + 𝑊 𝑷𝟐 𝑄 = 𝛥𝑈 + 𝑊 − 𝑊 ∆𝑺 = 𝒎𝑪𝒗𝒍𝒏 𝑷𝟏 Hence, for constant volume process 𝑸 = ∆𝑼 − 𝑾𝒑 Isometric Process, V=C PV – T relation 𝑷𝟏 𝑷𝟐 = 𝑻𝟏 𝑻𝟐 Change in Internal Energy ∆𝑼 = 𝒎𝑪𝒗 ∆𝑻 Change in Enthalpy ∆𝑯 = 𝒎𝑪𝒑∆𝑻 𝑾𝒏 𝒇 = 𝟎 Work Non- Flow Work Steady – Flow W = −𝛥𝑃𝐸 − ∆𝐾𝐸 − ∆𝑃𝑉 Change in Entropy 𝑷𝟐 ∆𝑺 = 𝒎𝑪𝒗𝒍𝒏 𝑷𝟏 Isometric Process PV – T relation Change in Enthalpy = 𝐶; if V = constant 𝑑ℎ 𝑷𝟏 𝑷𝟐 𝐶𝑝 = = 𝑑𝑡 𝑻𝟏 𝑻𝟐 ∆𝑯 = 𝒎𝑪𝒑∆𝑻 Change in Internal Energy Work Non – Flow 𝐶 = ; 𝑑𝑢 = 𝐶 𝑑𝑡 𝑊 = 𝑃𝑑𝑉 ; 𝑉 = 𝐶 ∆𝑼 = 𝒎𝑪𝒗 ∆𝑻 𝑾𝒏𝒇 = 𝟎 Isometric Process Work Steady – Flow Considering Ideal Gas Equation; 𝑃𝑣 = 𝑚𝑅𝑇 W = −𝛥𝑃𝐸 − ∆𝐾𝐸 − ∆𝑃𝑉 𝐖𝒔𝒇 = −𝒎𝑹∆𝑻 If 𝛥𝑃𝐸 & ∆𝐾𝐸 is neglected, therefore W = −𝑉 ∆𝑃 W =− vdP −𝑽 ∆𝑷 = − 𝒗𝒅𝑷  For non – flow system with paddle work (𝑊 ) considering figure, Isometric Process Change in Entropy 𝑄 𝑆= ∆𝑇 𝑑𝑄 𝑚𝐶𝑣𝑑𝑇 ∆𝑆 = = ∆𝑇 𝑇 ∆𝑆 = 𝑚𝐶𝑣𝑙𝑛 ; = 𝑄 + 𝑊 = 𝛥𝑈 + 𝑊 𝑷𝟐 𝑄 = 𝛥𝑈 + 𝑊 − 𝑊 ∆𝑺 = 𝒎𝑪𝒗𝒍𝒏 𝑷𝟏 Hence, for constant volume process 𝑸 = ∆𝑼 − 𝑾𝒑 Isometric Process, V=C PV – T relation 𝑷𝟏 𝑷𝟐 = 𝑻𝟏 𝑻𝟐 Change in Internal Energy ∆𝑼 = 𝒎𝑪𝒗 ∆𝑻 Change in Enthalpy ∆𝑯 = 𝒎𝑪𝒑∆𝑻 𝑾𝒏 𝒇 = 𝟎 Work Non- Flow Work Steady – Flow W = −𝛥𝑃𝐸 − ∆𝐾𝐸 − ∆𝑃𝑉 Change in Entropy 𝑷𝟐 ∆𝑺 = 𝒎𝑪𝒗𝒍𝒏 𝑷𝟏 Relation of Specific heat ratio in Ideal Gas If =k If =k Where: C = C k and C = C +R Where: C = and C = C + R C = +R C k= C +R C − =R C k−C =R C 1− =R C =R C k−1 =R 𝐑𝐤 𝐂𝐯 = 𝐑 𝐂𝐩 = (𝐤 𝟏) 𝐤−𝟏 Combined Gas Law = constant = 𝒎𝑹 𝑷𝒗 = 𝒎𝑹 𝑻 R = Gas Constant its value is 8.3143 kJ/kg mol K Specific Heat Capacities of Ideal Gas If at constant Volume System If at constant Pressure System Q = mC ∆T = ∆U Q = mC ∆T = ∆H