Thermodynamics: An Engineering Approach
9th Edition
ISBN: 9781259822674
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 12.6, Problem 84RP
Using the cyclic relation and the first Maxwell relation, derive the other three Maxwell relations.
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Chapter 12 Solutions
Thermodynamics: An Engineering Approach
Ch. 12.6 - What is the difference between partial...Ch. 12.6 - Consider the function z(x, y). Plot a differential...Ch. 12.6 - Consider a function z(x, y) and its partial...Ch. 12.6 - Prob. 4PCh. 12.6 - Prob. 5PCh. 12.6 - Consider a function f(x) and its derivative df/dx....Ch. 12.6 - Conside the function z(x, y), its partial...Ch. 12.6 - Consider air at 350 K and 0.75 m3/kg. Using Eq....Ch. 12.6 - Consider air at 350 K and 0.75 m3/kg. Using Eq....Ch. 12.6 - Nitrogen gas at 800 R and 50 psia behaves as an...
Ch. 12.6 - Consider an ideal gas at 400 K and 100 kPa. As a...Ch. 12.6 - Using the equation of state P(v a) = RT, verify...Ch. 12.6 - Prove for an ideal gas that (a) the P = constant...Ch. 12.6 - Verify the validity of the last Maxwell relation...Ch. 12.6 - Verify the validity of the last Maxwell relation...Ch. 12.6 - Show how you would evaluate T, v, u, a, and g from...Ch. 12.6 - Prob. 18PCh. 12.6 - Prob. 19PCh. 12.6 - Prob. 20PCh. 12.6 - Prove that (PT)=kk1(PT)v.Ch. 12.6 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Using the Clapeyron equation, estimate the...Ch. 12.6 - Prob. 26PCh. 12.6 - Determine the hfg of refrigerant-134a at 10F on...Ch. 12.6 - Prob. 28PCh. 12.6 - Prob. 29PCh. 12.6 - Two grams of a saturated liquid are converted to a...Ch. 12.6 - Prob. 31PCh. 12.6 - Prob. 32PCh. 12.6 - Prob. 33PCh. 12.6 - Prob. 34PCh. 12.6 - Prob. 35PCh. 12.6 - Prob. 36PCh. 12.6 - Determine the change in the internal energy of...Ch. 12.6 - Prob. 38PCh. 12.6 - Determine the change in the entropy of helium, in...Ch. 12.6 - Prob. 40PCh. 12.6 - Estimate the specific heat difference cp cv for...Ch. 12.6 - Derive expressions for (a) u, (b) h, and (c) s for...Ch. 12.6 - Derive an expression for the specific heat...Ch. 12.6 - Derive an expression for the specific heat...Ch. 12.6 - Derive an expression for the isothermal...Ch. 12.6 - Prob. 46PCh. 12.6 - Show that cpcv=T(PT)V(VT)P.Ch. 12.6 - Show that the enthalpy of an ideal gas is a...Ch. 12.6 - Prob. 49PCh. 12.6 - Show that = ( P/ T)v.Ch. 12.6 - Prob. 51PCh. 12.6 - Prob. 52PCh. 12.6 - Prob. 53PCh. 12.6 - Prob. 54PCh. 12.6 - Prob. 55PCh. 12.6 - Does the Joule-Thomson coefficient of a substance...Ch. 12.6 - The pressure of a fluid always decreases during an...Ch. 12.6 - Will the temperature of helium change if it is...Ch. 12.6 - Estimate the Joule-Thomson coefficient of...Ch. 12.6 - Estimate the Joule-Thomson coefficient of...Ch. 12.6 - Prob. 61PCh. 12.6 - Steam is throttled slightly from 1 MPa and 300C....Ch. 12.6 - What is the most general equation of state for...Ch. 12.6 - Prob. 64PCh. 12.6 - Consider a gas whose equation of state is P(v a)...Ch. 12.6 - Prob. 66PCh. 12.6 - What is the enthalpy departure?Ch. 12.6 - On the generalized enthalpy departure chart, the...Ch. 12.6 - Why is the generalized enthalpy departure chart...Ch. 12.6 - What is the error involved in the (a) enthalpy and...Ch. 12.6 - Prob. 71PCh. 12.6 - Saturated water vapor at 300C is expanded while...Ch. 12.6 - Determine the enthalpy change and the entropy...Ch. 12.6 - Prob. 74PCh. 12.6 - Prob. 75PCh. 12.6 - Prob. 77PCh. 12.6 - Propane is compressed isothermally by a...Ch. 12.6 - Prob. 81PCh. 12.6 - Prob. 82RPCh. 12.6 - Starting with the relation dh = T ds + vdP, show...Ch. 12.6 - Using the cyclic relation and the first Maxwell...Ch. 12.6 - For ideal gases, the development of the...Ch. 12.6 - Show that cv=T(vT)s(PT)vandcp=T(PT)s(vT)PCh. 12.6 - Temperature and pressure may be defined as...Ch. 12.6 - For a homogeneous (single-phase) simple pure...Ch. 12.6 - For a homogeneous (single-phase) simple pure...Ch. 12.6 - Prob. 90RPCh. 12.6 - Prob. 91RPCh. 12.6 - Estimate the cpof nitrogen at 300 kPa and 400 K,...Ch. 12.6 - Prob. 93RPCh. 12.6 - Prob. 94RPCh. 12.6 - Prob. 95RPCh. 12.6 - Methane is to be adiabatically and reversibly...Ch. 12.6 - Prob. 97RPCh. 12.6 - Prob. 98RPCh. 12.6 - Prob. 99RPCh. 12.6 - An adiabatic 0.2-m3 storage tank that is initially...Ch. 12.6 - Prob. 102FEPCh. 12.6 - Consider the liquidvapor saturation curve of a...Ch. 12.6 - For a gas whose equation of state is P(v b) = RT,...Ch. 12.6 - Prob. 105FEPCh. 12.6 - Prob. 106FEP
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- (4)Derive following relation between Cp and Cv using the method of Jacobians C,-C, = B*VT / Karrow_forward1. One mole of an ideal gas at 10 atm pressure is contained in a vessel at 300K. The gas is expanded till the pressure becomes 2 atm and the temperature reaches 400K. Calculate the work done on the system and the heat absorbed by it if the change is brought about by the following processes:A] The gas is expanded isothermally against a constant external pressure of 2 atm, then heated to the desired temperature at constant volume, and finally expanded till the final state is reached.B] The gas is expanded by an isothermal reversible process, then heated to 400K, and again expanded reversibly till he final state is reached.C] The gas is first heated in an isochoric process and then expanded reversibly in an isothermal process.arrow_forward2. The gas expanding in the combustion space of a reciprocating engine has an initial pressure of 5o bar and an initial temperature of 1623 C. The initial volume is 50000 mm' and the gas expands through a volume ratio of 20 according to the law pV = constant. Calculate w and AU Take R = 270 J/Kg K and C, = 800 J/Kg K. Assume n = 1.38arrow_forward
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- Q4: Sulphur dioxide produced by the combustion of sulphur in air is absorbed in water. Pure SO₂ is then recovered from the solution by steam stripping. Make a preliminary design for the absorption column. The feed will be 5000 kg/h of gas containing 8 per cent v/v SO₂. The gas will be cooled to 20°C. A 95 per cent recovery of the sulphur dioxide is required. Use Cornell's method. Data: NOG-8, Mwt gas-29, Water flow rate-29.5 kg/s, Fp = 170 m, py= 1.21 kg/m³, . pressure drop = 20 mm H₂O/m packing, HL= 10-³ N s/m² D₁ = 1.7 x 10-9 m²/s, Dy = 1.45 x 10-5 m²/s, y = 0.018 x 10-3 Ns/m² Useful formulas: HG = 0.011 Uh (Sc)85 (0 0.305, H₂ = 0.305 h (Sc) 0,5 K3 1:11 Z 3.05, 0.33 Z (305) /(Liv f₂f2₂63) 0.5 0.15 3arrow_forwardQ4: Sulphur dioxide produced by the combustion of sulphur in air is absorbed in water. Pure SO₂ is then recovered from the solution by steam stripping. Make a preliminary design for the absorption column. The feed will be 5000 kg/h of gas containing 8 per cent v/v SO₂. The gas will be cooled to 20°C. A 95 per cent recovery of the sulphur dioxide is required. Use Cornell's method. Data: NOG-8, Mwt gas-29, Water flow rate=29.5 kg/s, Fp = 170 m¹, Py = 1.21 kg/m³, pressure drop 20 mm H₂O/m packing, HL= 10-3 N s/m², D₁ = 1.7 x 10⁹ m²/s, D, = 1.45 x 10-5 m²/s, y = 0.018 x 10³ Ns/m² Useful formulas: HG = 0.011 h (Sc)0.5 Dc 0.305/ H₁ = 0.305 h (Sc)2.5 K3 1.11 Z 3.05/ Z 9/1 0.15 0.33 3.05/ / (Lw f1f₂f3)0.5arrow_forwardDerive energy equation from the first law of thermodynamic with detailed steps on how the dissipation function was obtainedarrow_forward
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