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Chapter 14: Problem 6

What do \((a)\) homogeneous reactions and \((b)\) heterogeneous reactions represent in mass transfer? To what do they correspond in heat transfer?

Short Answer

Expert verified
Answer: Homogeneous reactions in mass transfer occur between substances in the same phase, with the reactants and products uniformly distributed within a single phase. The corresponding concept in heat transfer is conduction, which is the transfer of heat within a single-phase material driven by temperature gradients. Heterogeneous reactions in mass transfer occur at the interface between substances in different phases, with the reactants and products not uniformly distributed. The corresponding concept in heat transfer is convection, which is the transfer of heat by the movement of fluids due to temperature gradients, either by forced or natural circulation. The heat transfer process in convection depends on both the temperature gradients and the surface properties of the interface.

Step by step solution

01

(a) Homogeneous Reactions

Homogeneous reactions in mass transfer are chemical reactions that occur between substances in the same phase (solid, liquid, or gas). All the reactants and products are uniformly distributed within a single phase, and the mass transfer is primarily driven by concentration gradients within that phase. Now, we are going to find the corresponding concept in heat transfer.
02

(a) Corresponding Concept in Heat Transfer

The corresponding concept of homogeneous reactions in heat transfer is conduction. Conduction is the transfer of heat within a single-phase material, either solid, liquid, or gas, due to temperature gradients within the material. It can occur in any of these phases without a significant change in the material's physical state. Conduction is driven by temperature gradients, similarly to how concentration gradients drive mass transfer in homogeneous reactions.
03

(b) Heterogeneous Reactions

Heterogeneous reactions in mass transfer are chemical reactions that occur at the interface between substances in different phases (solid, liquid, or gas). In these reactions, mass transfer occurs across the boundary separating the phases, and the reactants and products are not uniformly distributed. The mass transfer in such reactions is driven by concentration gradients between the phases and the surface properties of the interface. Now, we are going to find the corresponding concept in heat transfer.
04

(b) Corresponding Concept in Heat Transfer

The corresponding concept of heterogeneous reactions in heat transfer is convection. Convection is the transfer of heat by the movement of fluids (liquid or gas) in response to temperature gradients. In convection, heat is exchanged between different phases or across the boundary separating the phases, similarly to heterogeneous reactions in mass transfer. The fluid circulation can be driven by external forces (forced convection) or by buoyancy forces caused by density variations (natural convection). The heat transfer process in convection is dependent on both the temperature gradients and the surface properties of the interface.

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Most popular questions from this chapter

You probably have noticed that balloons inflated with helium gas rise in the air the first day during a party but they fall down the next day and act like ordinary balloons filled with air. This is because the helium in the balloon slowly leaks out through the wall while air leaks in by diffusion. Consider a balloon that is made of \(0.1\)-mm-thick soft rubber and has a diameter of \(15 \mathrm{~cm}\) when inflated. The pressure and temperature inside the balloon are initially \(110 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). The permeability of rubber to helium, oxygen, and nitrogen at \(25^{\circ} \mathrm{C}\) are \(9.4 \times 10^{-13}, 7.05 \times 10^{-13}\), and \(2.6 \times 10^{-13} \mathrm{kmol} / \mathrm{m} \cdot \mathrm{s} \cdot\) bar, respectively. Determine the initial rates of diffusion of helium, oxygen, and nitrogen through the balloon wall and the mass fraction of helium that escapes the balloon during the first \(5 \mathrm{~h}\) assuming the helium pressure inside the balloon remains nearly constant. Assume air to be 21 percent oxygen and 79 percent nitrogen by mole numbers and take the room conditions to be \(100 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\).

Hydrogen gas at \(750 \mathrm{kPa}\) and \(85^{\circ} \mathrm{C}\) is stored in a spherical nickel vessel. The vessel is situated in a surrounding of atmospheric air at \(1 \mathrm{~atm}\). Determine the molar and mass concentrations of hydrogen in the nickel at the inner and outer surfaces of the vessel.

A recent attempt to circumnavigate the world in a balloon used a helium-filled balloon whose volume was \(7240 \mathrm{~m}^{3}\) and surface area was \(1800 \mathrm{~m}^{2}\). The skin of this balloon is \(2 \mathrm{~mm}\) thick and is made of a material whose helium diffusion coefficient is \(1 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\). The molar concentration of the helium at the inner surface of the balloon skin is \(0.2 \mathrm{kmol} / \mathrm{m}^{3}\) and the molar concentration at the outer surface is extremely small. The rate at which helium is lost from this balloon is (a) \(0.26 \mathrm{~kg} / \mathrm{h}\) (b) \(1.5 \mathrm{~kg} / \mathrm{h}\) (c) \(2.6 \mathrm{~kg} / \mathrm{h}\) (d) \(3.8 \mathrm{~kg} / \mathrm{h}\) (e) \(5.2 \mathrm{~kg} / \mathrm{h}\)

What is a concentration boundary layer? How is it defined for flow over a plate?

Consider a 20 -cm-thick brick wall of a house. The indoor conditions are \(25^{\circ} \mathrm{C}\) and 50 percent relative humidity while the outside conditions are \(50^{\circ} \mathrm{C}\) and 50 percent relative humidity. Assuming that there is no condensation or freezing within the wall, determine the amount of moisture flowing through a unit surface area of the wall during a \(24-\mathrm{h}\) period.
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