Chapter 3

When can a system be considered in "steady state"?

Using Equation (3.6), derive a material balance for a reactant in a closed system.

What is the difference between an open system and a closed system?

For a reaction mixture with a density that is linearly dependent on the conversion, with \(\rho=\rho_{0}\left(1+\varepsilon \zeta_{A}\right)\), derive a relation for the concentration of species \(\mathrm{A}\left(\mathrm{c}_{A}\right)\) as a function of the relative degree of conversion \(\zeta_{A}\).

What is the difference between microscopic and macroscopic balances? For which situations in general do you use each of both approaches?

The cavitation number is defined as \(C a=\frac{p-p_{\text {vap }}}{(1 / 2) \rho \mathrm{v}^{2}}\). Now, for ethanol produced by sugar fermentation, a company has installed a pump for the transport of the liquid product, which is assumed to be pure. The ambient pressure is \(1020 \mathrm{hPa}\) and the pump is situated \(1 \mathrm{~m}\) below a vessel from which the product is pumped through a duct of \(10 \mathrm{~cm}\) diameter with a mass flow rate of \(25 \mathrm{t} \cdot \mathrm{h}^{-1}\). The temperature at the pump suction side is \(20^{\circ} \mathrm{C}\). At this temperature, the vapor pressure is \(5.7 \times 10^{3} \mathrm{~Pa}\). The density of ethanol is 789 \(\mathrm{kg} \cdot \mathrm{m}^{-3}\). What is the background of cavitation? Does it occur in this situation? Which assumption(s) have you made? When will there be a possibility for this phenomenon to occur?

What is the difference between the "degree of conversion" and the "relative degree of conversion" for a chemical reaction \(2 \mathrm{~A} \rightarrow \mathrm{B}\) ? What changes when the degree of conversion is expressed on a molar basis?

In the energy balance, the change in potential energy is usually based on the gravity field; which other fields might be relevant as well and which terms would then appear?

A steam boiler drum produces steam at a mass flow rate of \(64 \mathrm{~kg} \cdot \mathrm{s}^{-1}\) at 60 bar. This stream still contains \(2 \mathrm{wt} \%\) moisture. The feedwater from the economizer (a heat exchanger) is fed to the drum at a mass flow rate of \(62 \mathrm{~kg} \cdot \mathrm{s}^{-1}\). It contains \(3 \mathrm{ppm}_{\mathrm{w}}\) solids. Makeup water, containing \(50 \mathrm{ppm}_{\mathrm{w}}\) solids, is also fed into the drum at a mass flow rate of \(2 \mathrm{~kg} \cdot \mathrm{s}^{-1}\). Steam production is such that the solid content of the moisture leaving with the steam is \(5 \mathrm{ppm}_{\mathrm{w}}\). Blowdown, which is the release of hot liquid from the bottom of the drum, must keep the concentration of solids in the drum to \(1000 \mathrm{ppm}_{\mathrm{w}}\) - a. Calculate the blowdown requirement in \(\mathrm{kg} \cdot \mathrm{s}^{-1}\). b. Calculate the heat loss associated with blowdown in \(\mathrm{kW}\).

Indicate whether the following statements are in general true or false: \- Enthalpy is always conserved. \- Momentum is always conserved. \- The number of moles of a chemical component is always conserved in a chemical reaction. \- The mass of each element is conserved during combustion of biomass.

Power company "E" in the Netherlands operates a fluidized bed combustion-based boiler with wood residues as fuel. The plant contains a simple steam turbine. The steam conditions at the inlet of the turbine are \(525^{\circ} \mathrm{C}\) and 100 bar. Assume that condensation of the steam takes place at a temperature of \(20^{\circ} \mathrm{C}\) and that isentropic expansion of steam occurs in the turbine. a. What is the specific power \(\left(\mathrm{kJ} \cdot \mathrm{kg}^{-1}\right)\) of the turbine expansion process? b. If the power plant generates \(25 \mathrm{MW}_{\mathrm{e}}\) and water pump work can be neglected, what is the mass flow rate of steam through the turbine? c. What assumptions have you made for these calculations?

Bio-oil flows through a duct with a radius of \(2.5 \mathrm{~cm}\) at ambient temperature with a velocity \(\left(\mathrm{v}_{1}\right)\) of \(10 \mathrm{~m} \cdot \mathrm{s}^{-1}\); the duct is followed by a permeable wall part with suction. At the end of this section (with the same radius), the velocity \(\left(\mathrm{v}_{2}\right)\) has dropped to \(8 \mathrm{~m} \cdot \mathrm{s}^{-1}\). If \(p_{1}=140 \mathrm{kPa}\), estimate \(p_{2}\) for the case that wall friction is negligible. What happens to \(p_{2}\) in the case of significant friction?

An anaerobic digester (see Chapter 14 for this technology) produces biogas at \(1.1\) bar (absolute) and \(25^{\circ} \mathrm{C}\). This gas, composed of 60 vol. \(\% \mathrm{CH}_{4}\) and 40 vol. \(\% \mathrm{CO}_{2}\), is to be compressed to 25 bar (absolute) before delivery to its end use; assume the compression to be isentropic and reversible. Calculate the temperature after compression.

Determine the adiabatic, stoichiometric flame temperature at constant pressure for n-butanol, an alternative biofuel, give \((25 \mathrm{C}, 1 \mathrm{~atm})\) the enthalpy of combustion is \(-26\)