Consider a gas that follows the equation of state P (V - B) = RT where b is a constant. If the compressibility factor Z = PV/RT is equal to Z= 0.85 at temperature T=50 C what is the value of the residual enthalpy. Express your result in kJ/kmol
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Consider a gas that follows the equation of state P (V - B) = RT where b is a constant. If the compressibility factor Z = PV/RT is equal to Z= 0.85 at temperature T=50 C what is the value of the residual enthalpy. Express your result in kJ/kmol
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- We know that for an ideal gas Cp,m = Cv,m + R. %3D The general relationship for any gas can be written, for 1 mole, as Cp,m = Cy,m + (Yn") a²VmT` k (equation-1) Where Vm is the molar volume (the volume of 1 mole of the gas, V/n). a is the coefficient of volume expansion and is given by: a = where the partial derivative of V with respect to T is calculated ƏT assuming P is constant And K is the coefficient of volume expansion and is given by: k = GO where the partial derivative of V with respect to P is calculated assuming T is constant. Note the minus in the definition. Prove that equation-1 reduces to the result derived in class for an ideal gas by calculating (A²V¼T\ kStarting from the fundamental thermodynamic equation, a) derive (OP) in terms of P, T, and V. T b) derive (o) for a vdW gas assuming that the ӘР T PV compressibility factor is z = = 1+ + P (b-a) RT RT RT c) calculate the enthalpy change (in J) for the isothermal increase in pressure from 3 atm to 15 atm of a mole of vdW gas at 25 °C. (a = 1.361 L² atm mol-2; b= 0.0318 L mol-¹)Two moles of an ideal gas (Cv,m = 19.7 JK¯¹ mol¯¹) originally in state 1 are taken through three reversible steps A, B, and C indicated on the following plot of pV versus p: pV/Lbar 44.8 22.4 A C B 4 p/bar 2 Calculate q, w, AU and AH for the individual steps AND for the complete cycle. Then tabulate your results with "q, w, AU and AH” as column headings and "A, B, C and Cycle" as the row headings.
- Find AS (cal/K) when 6.4 mol of some gas O2 is heated from 1.2 K to 2.4 K with P held fixed at 1.00 atm. Where Cpm=a+bT,where value of a=9.46 cal.mol1K1 and b=0.00135 cal.mol1K2. Answer:1) Show that for ideal gas: [dH= Cp dT] and dS= Cp dT/T-R dP 1 Add file11. For a certain ideal gas, the increase of enthalpy is 34 Kcal when the pressure increases from 0.11 MPaa to 1.1 MPaa and the volume increases from 12.6 gallons to 19.7gallons. Determine (a) AU and (b) T₂ if T₁ = 303 K.
- (6) Consider an ideal gas for which pV = n RT. Determine the change in pressure, p, for n = 2.0 moles of an ideal gas when the temperature, T, is changed from 190K to 200K and the volume, V, is changed from 20L to 19L. The gas constant is R = 8.314 J• mol-1 • K-1. Express your answer in atmospheres. HINT: Use an expression for the total differential dp(T, V). Evaluate your partial derivatives at the point (V,, T¡) with the increments in volume dV = (V, – V,) and dT = (T, – T,)EXERSICE 1 An ideal gas undergoes a process A -> B in two alternative ways: i) reversible and ii) irreversible. Which of the following options are always correct? Provide a brief and sufficient justification for your selections and exclusions. The symbol S refers to the ideal gas System unless the Universe is explicitly referred to as the Suniverse. ASrev. = 0 ASirrev>0 AS Suniverse |rev = 0 ASuniverse rev 0 ASaçx.Find AS (cal/K) when 6.5 mol of some gas 02 is heated from 6.6 K to 6.1 K with P held fixed at 1.00 atm. Where Cp.m = a+bT , where value of a=2.91 cal.mol-K-1 and b=0.00521 cal.mol-1K-2. Answer: AnswerQuestion 1: (a) An ideal gas is expanded reversibly and ad- iabutically. Decide which of q. w, AU, and AH are pos- itive, negative, or zero. (b) A 1.25 mole sample of an ideal gas is expanded from 320. K and an initial pressure of 3.10 bar to a final pressure of 1.00 bar, und Cr- SR/2. Calculate w for the following two cases: Condition: The expansion is isothermal and reversible.Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kg, Q, T, U, and Up.) P = - -(3+), T - (ain(@)), КВТ = KBT Step 4 of 7 For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.) (3V)₁ = 1 UT 0 Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the translational partition function needs to be considered for an ideal monatomic gas. (Use the following as necessary: e, h, kg, m, N, T, T, and V.) N (2πmkBT) Ve Nh³ Q = (2µmkµT)h³v X Step 6 of 7 Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kB, M, N, π, T, and V.) Ve In(Q) N In (2μmkBT) Nh³ (2π m kBT) e N ln (V) + Nln Nh³ Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kg, m, N, π, T, and V.) NKB T P = V |KBTN- V Step 7 of 7 Rearrange the equation for P from Step…Q\4: Combustion 0.1 mole of propane in bomb calorimeter with excess amount of oxygen represented by reaction C3H8 (g) +50₂ (g) → 3C0₂(g) + 4H₂0 (1) If initial temp. of calorimeter was 25 C° & total thermal capacity 97.1 KJ.C-1. The reaction leaded temp. rose to 27.282 C°. Determine AH & AE in unit of 1 mole C3H8 KJSEE MORE QUESTIONS