Another equation of state is the Berthelot equation, V = RT/P + b - a/(RT2). Derive expressions for the coefficients of thermal expansion and isothermal compressibility for a Berthelot gas in terms of V, T, and P. 1 α = --(7), -(017), B= 1 (OV V OP ), =- Inv OP
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- 1. A perfect gas undergoes compression at constant temperature, which reduces its volumeby 3.08 dm3. The final pressure and volume of the gas are 6.42 bar and 5.38 dm3, respectively. Calculate the original pressure of the gas in (a) bar, (b) atm. 2. Consider an isothermal column of an ideal gas at 25oC. What must be the molar mass ofthis gas be if the pressure is 0.80 of its ground level value at (a) 10km and (b) 1km ? Please show complete solutionsPredict the output of energy as heat from the combustion of 1.0 dm3 of octane at 298 K and 1 bar. Its mass density is 0.703 g cm−3.. A 2.50 mole sample of a perfect gas for which Cv,m = 3R/2 (assume constant over T-range) undergoes the following two-step process: (1) from an initial state of the gas described by T = 13 ºC and P = 1.75 x 105 Pa, the gas undergoes an isothermal expansion against a constant pressure of 3.75 x 104 Pa until the volume has doubled. (2) subsequently, the gas is cooled at constant volume. The temperature falls to -24ºC. Calculate q, w, ∆U, and ∆H for each step and for the overall process.
- A fuel has the following volumetric analysis: CH4 = 68% C2H6 = 32% Assume complete combustion with 15% excess aur at 101.325 kPa and 27 degrees dry bulb temperature. What is the total moles in the products of combustion?An automobile wheel contains air with a pressure of 3x105 Pa at 25 ° C. The sipop cover was removed and the air was expanded adiabatically against an external pressure of 105 Pa. What is the final temperature of the gas in the wheel? (Take into account that the gas behaves ideally and the Cp value for air is 7 / 2R)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 Please respond ASAP
- The heat capacity ratio of an ideal gas is 1.38. What are its Cv and Cp values?An automobile wheel contains air with a pressure of 3x10^5 Pa at 25 ° C. The sipop cover was removed and the air was expanded adiabatically against an external pressure of 105 Pa. What is the final temperature of the gas in the wheel? (It should be taken into account that the gas behaves ideally and the Cp value for air is 7 / 2R)Ethene (C2H4) at 77oF undergoes complete combustion with stoichiometric air at 77oF and 70% humidity in an insulated steady-flow combustion chamber. Estimate the exit temperature assuming a pressure of 14.5 psia.
- A gas mixture at 300K and 1 bar analyzing by volume 20% N2 and 80% CH4 is subjected to liquefaction at the rate of 1500 kg/hr. It is found that only 30% (weight) of the entering gas is liquefied and the concentration of N2 in the liquid is 60% by weight. The unliquefied gas leaves the unit at 273K and 1 bar. Determine (a) the volume of the unliquefied gas, m3/hr (b) the composition of the gas leaving expressed as volume %.1.65 mol of a perfect gas for which Cv,m = 12.47 J K–1 mol–1 is subjected to two successive changes in state: (1) from 37.0 oC and 1.00´105 Pa, the gas is expended isothermally against a constant pressure of 16.5´103 Pa to twice its initial volume. (2) At the end of the previous process, the gas is cooled at constant volume from 37.0 oC to - 23.0 oC. (a) Calculate q , w , DU, DH for each of the stages.Cp− ̄Cv=T ̄V β^2/κ reduces to ̄CP− ̄CV=R for an ideal gas.