Calculate the molar volume and the compressibility factor of ethylene at 100 deg

Question

Calculate the molar volume and the compressibility factor of ethylene at 100 degree C and 20 bar. What is the standard heat of combustion of n heptane gas at 25 degree C if the combustion produces water?^2 Determine the heat transfer (in J mol^-1) when water is heated in steady flow process from 25 500 degree C at atmospheric pressure. Show that the entropy change of an ideal gas, with a gas constant R and constant heat capacity undergoing a mechanical reversible work in a closed system from (T_a, P_a) to (T, P) is given expression:^3 [Delta S = integral_r^r C_r^s dT/T - R ln [P/P_0]] One kg of air (M_a = 29 g mol^-1, C_p = 21 J mol^-1 K^-4) is compressed from (25 degree C, 10 bar) to in a frictionless piston cylinder. Assuming that air behaves as an ideal gas, calculate the energy, enthalpy and entropy changes. An inventor claims to have devised a cyclic engine which exchanges heat with reservoirs at 25 250 degree C, and which produces 0.45 kJ of work for each kJ of heat extracted from the hot reservoir claim believable? Why or why not?^3 A heat engine receives 800 kJ of heat from a high temperature source at 900 degree C during a converts 250 kJ of this heat to net work (W) and rejects the remaining quantity of energy temperatures sink at 30 degree C. How much heat is rejected to the low temperatures reservoir?^2 Determine if this heat engine violates the second law of thermodynamics on the basis The Carnot principle, ^2 The Clausius inequality, ^2

Explanation / Answer

Calculate the molar volume and the compressibility factor of ethylene at 100 C and 20 bar

Density of ethylene = 1.18 kg/m³ = 1.18 g/ L

Now calculate the mole / L of ethylene gas at given temperassure and pressure as follows:

n / V = P / RT

here P = 20 bar = 19.7385 atm

Temperature T = 100 C = 100++273 = 373 K

Therefore;

n / V = P / RT

= (19.7385 atm) / ((0.08206 Latm/Kmol) x (373 K))

= 0.645 mol/L for an ideal gas

Now from the density and molar maas:

Molar mass of ethylene = 28.05 g/mol
Therefore;

n / V =density in g/L / Molar mass in g/ mole

= 1.18 g/ L/28.05 g/mol

= 0.0421 mol/L for Ethylene sample

The compressibility factor (Z), is the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure.
Z = (0.0421 mol/L) / (0.645 mol/L)

= 0.065

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