# Heat Transfer Operations Questions and Answers – Dryers – Moisture Isotherms

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This set of Heat Transfer Operations Quiz focuses on “Dryers – Moisture Isotherms”.

1. The lower the relative humidity _________ is the moisture bound to the host material.
a) Weaker
b) Stronger
c) More quantity
d) Less volume

Explanation: The lower the relative humidity, the more strongly is the moisture bound to the host material because the free moisture from the surface has been already lost and the interior layers of moisture are hence strongly bound.

2. The free energy ΔG required to release unit molal quantity of this moisture is given by ___________
a) – RT Ln(Relative Humidity)
b) – RT Ln(Mole fraction of water)
c) – RT Ln(Moisture content)
d) – RT Ln(Absolute Humidity)

Explanation: The free energy ΔG required to release unit molal quantity of this moisture is given by the equation, ΔG = – RT Ln(HR) where HR is the relative humidity.

3. What is the term Ψ in the given equation of free energy ΔG required to release unit molal quantity of this moisture?
ΔG = – RT Ln(Ψ)
a) Absolute Humidity
b) Relative Humidity
c) Mole fraction of water
d) Moisture content

Explanation: The free energy ΔG required to release unit molal quantity of this moisture is given by the equation, ΔG = – RT Ln(Ψ), where Ψ is the relative humidity. The definition of relative humidity is the ratio of the moisture-vapour pressure to the saturation value at the same temperature.
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4. The free energy ΔG required to release unit molal quantity of this moisture is given by
ΔG = – RT Ln(Ψ), for an isothermal, reversible process without change of composition.
a) True
b) False

Explanation: Yes, the statement is true. This standard equation of Gibbs free energy can only be applied for an isothermal, reversible process without change of composition.

5. Isothermal variation of the equilibrium moisture content which is a function of this free-energy change with relative humidity yields a ____________
a) Langmuir isotherm
b) Moisture isotherm
d) Pressure isotherm

Explanation: The moisture isotherm is the plot of the relationship between water content and equilibrium relative humidity of a material at equilibrium.

6. Moisture isotherms are normally _________ in shape when plotted over the whole relative humidity range.
a) Sigmoid
b) Exponential
c) Parabolic
d) Hyperbolic

7. Which one of the following isotherm is of prime interest in drying?
a) Langmuir isotherm
b) Desorption isotherm
c) Moisture isotherm

8. Consideration of multi-molecular adsorption leads to an equation given below for moisture content.
a) $$\frac{X}{X_1} =\frac{C\phi}{(1-k\phi)(1+(C-k)\phi)}$$
b) $$\frac{X}{X_1} =\frac{C\phi}{(1+k\phi)(1+(C-k)\phi)}$$
c) $$\frac{X}{X_1} =\frac{C\phi}{(1-k\phi)(1-(C-k)\phi)}$$
d) $$\frac{X}{X_1} =\frac{C\phi}{(1-k\phi)(1+(C+k)\phi)}$$

Explanation: $$\frac{X}{X_1} =\frac{C\phi}{(1-k\phi)(1+(C-k)\phi)}$$ is the required equation for multi-molecular adsorption, the terms are given in the equation are–

1. X: it is the moisture content at a relative humidity Ψ which is at equilibrium
2. X1: it is the moisture content for a single layer or monolayer
3. K: it is the expression e(± ΔH/RT), where ΔH is the enthalpy difference in adsorption heat quantity between the first and successive molecular moisture layers
4. C: it is an experimentally calculated coefficient.

9. What is the term X1 in the given equation?
$$\frac{X}{X_1} =\frac{C \phi}{(1-k \phi)(1+(C-k) \phi))}$$
a) Equilibrium moisture content
b) Moisture content for a complete layer
c) Moisture content for three layers together
d) Moisture content for a complete monolayer

Explanation: In the equation $$\frac{X}{X_1} =\frac{C \phi}{(1-k \phi)(1+(C-k) \phi))}$$ for multi-molecular adsorption, the terms are –

1. X: it is the moisture content at a relative humidity Ψ which is at equilibrium
2. X1: it is the moisture content for a single layer or monolayer
3. K: it is the expression e(± ΔH/RT), where ΔH is the enthalpy difference in adsorption heat quantity between the first and successive molecular moisture layers
4. C: it is an experimentally calculated coefficient.

10. What is the term K in the given equation of multi-molecular adsorption?
$$\frac{X}{X_1} =\frac{C\phi}{(1-k\phi)(1+(C-k)\phi)}$$
a) k is the relative humidity
b) k is the exp (± ΔH/RT)
c) k is the moisture content for a complete layer
d) k is the enthalpy difference in adsorptive heats between the first and successive molecular layers

Explanation: In the equation $$\frac{X}{X_1} =\frac{C\phi}{(1-k\phi)(1+(C-k)\phi)}$$ for multi-molecular adsorption, the terms are –

1. X: it is the moisture content at a relative humidity Ψ which is at equilibrium
2. X1: it is the moisture content for a single layer or monolayer
3. K: it is the expression e(± ΔH/RT), where ΔH is the enthalpy difference in adsorption heat quantity between the first and successive molecular moisture layers
4. C: it is an experimentally calculated coefficient.
Explanation: The moisture isotherms are sigmoid functions and hence the other two options are totally incorrect, the one with the adsorption isotherm above it is the correct option as the desorption isotherm has lesser moisture content than its counter-part.

12. What is the definition of relative humidity?
a) $$\frac{Actual\, vapour\, density}{saturation \, vapour\, density}$$
b) $$\frac{Actual \, vapour \, density}{minimum\, vapour\, density}$$
c) $$\frac{Saturation\, vapour \, density}{maximum \, vapour\, density}$$
d) $$\frac{Actual\, vapour\, density}{Theoretical\, vapour\, density}$$

Explanation: The Relative humidity is defined as – the amount of moisture in the air divided by the maximum amount of moisture that could exist in the air at a specific temperature.
Hence the correct formula is $$\frac{Actual\, vapour \, density}{saturation\, vapour\, density}$$

13. What is the name of the axes in the moisture isotherm plotted below? a) X – Relative humidity Y – Moisture content
b) X – Relative humidity Y – Equilibrium moisture content
c) X – Absolute humidity Y – Moisture content
d) X – Absolute humidity Y – Equilibrium moisture content

Explanation: The axis of the adsorption desorption moisture isotherms are so set that the adsorption isotherm is less than the desorption ones. Hence the correct axes are X – Relative humidity Y – Equilibrium moisture content.

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