Elementary Principles of Chemical Processes, Binder Ready Version
4th Edition
ISBN: 9781118431221
Author: Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher: WILEY

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Textbook Question
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Chapter 8, Problem 8.1P

8.1. The specific internal energy of formaldehyde (HCHO) vapor at 1 atm and moderate temperatures is given by the formula

U ^ ( J / m o l ) = 25.96 T + 0.02134 T 2

where T is in °C.

Calculate the specific internal energies of formaldehyde vapor at 0°C and 200°C. What reference temperature was used to generate the given expression for U ^

1. ?
2. The value of U calculated for 200°C is not the true value of the specific internal energy of formaldehyde vapor at this condition. Why not? (Him: Refer back to Section 7.5a.) Briefly state the physical significance of the calculated quantity.
3. Use the closed system energy balance to calculate the heat (J) required to raise the temperature of 3.0 mol HCHO at constant volume from 0°C to 200°C. List all of your assumptions.
4. From the definition of heat capacity at constant volume, derive a formula for C v ( T ) [ J / m o l ° C ] .

Then use this formula and Equation 8.3-6 to calculate the heat (J) required to raise the temperature of 3.0 mol of HCHO(v) at constant volume from 0°C to 200°C. [You should get the same result you got in Part (c).]

Expert Solution
Interpretation Introduction

(a)

Interpretation:

The specific internal energies of formaldehyde vapor and the temperature should be calculated.

Concept introduction:

In the thermodynamic closed system, the exchange of matter does not take place but heat can be exchanged and thus, the work done by the system is considered to be zero.

The specific internal energy of formaldehyde Vapor is given by:

UT=25.96T+0.02134T2

Where T= temperature of formaldehyde

0J/mol, 6046J/mol and 00C.

### Explanation of Solution

Calculate the internal energy of formaldehyde at 0 and 200° C as,

UT=25.96T+0.02134T2

U00C=25.960+0.0213402=0J/mol

U2000C=25.96200+0.021342002=6046J/mol

Since the reference temperature is that temperature at which internal energy becomes zero.

The reference temperature is 00C.

Expert Solution
Interpretation Introduction

(b)

Interpretation:

The importance of calculated quantity should be explained.

Concept introduction:

Thermodynamic closed system in which no exchange of matter takes place but the exchange of heat occurs then the work done by the system is considered to be zero.

The specific internal energy of formaldehyde Vapor is given by:

UT=25.96T+0.02134T2

Where T= temperature of formaldehyde

### Explanation of Solution

The calculation of the absolute value of internal energy for a process material is not possible. However, it is possible to estimate the change in internal energy for a defined change of state like solid, liquid or gas.

In part (a) calculation, the change in internal energy is calculated with references to 0 °C.

Expert Solution
Interpretation Introduction

(c)

Interpretation:

The heat required to raise the temperature for the given range by stating the assumptions should be calculated.

Concept introduction:

Thermodynamic closed system in which no exchange of matter takes place, but the exchange of heat occurs then the work done by the system is zero.

The specific internal energy of formaldehyde Vapor is given by:

UT=25.96T+0.02134T2

Where T= temperature of formaldehyde

18137J and assumptions of a closed system are as follows:

• Work done by the system is zero.
• Potential energy drop is zero.
• Kinetic energy drop is also 0.
• No moving parts in the system.
• There is no energy transfer to and from the system

### Explanation of Solution

From total energy balance,

Q+W=ΔU+ΔEK+ΔEP

Since the kinetic energy, potential energy and the work done are zero.

Q+0=ΔU+0+0

Using part (a),

ΔU=U1000CU00C=6046-0J/mol=6046J/mol

Therefore, total energy for the system is,

ΔU=6046J/mol3mol=18137J

Assumptions.

• Work done by the system is zero.
• Potential energy drop is zero.
• Kinetic energy drop is also 0.
• No moving parts in the system.
• There is no energy transfer to and from the system
Expert Solution
Interpretation Introduction

(d)

Interpretation:

A formula for Cv should be derived and it should be used to calculate the heat required for the given case.

Concept introduction:

Thermodynamic closed system in which no exchange of matter takes place, but the exchange of heat occurs then the work done by the system is zero.

The specific internal energy of formaldehyde Vapor is given by:

UT=25.96T+0.02134T2

Where T= temperature of formaldehyde

dUdT=Cv and 18137J.

### Explanation of Solution

Use the given equation,

ΔU=T1T2CvdT

Differentiate both sides,

dΔUdT=ddTT1T2CvdT

Rearranging the above equation,

dUdT=Cv

At constant volume,

CV=dUdTv

Apply the given values as,

CV=dUdT=d25.96T+0.04268T2dTJ/mol0C

Differentiate the equation as,

CV=25.96+0.04268TJ/mol0C

Finally, calculate the change of moles for the given case as,

ΔU=nHCHO020025.96+0.04268TdT=nHCHO25.96T+0.04268T2/20200=3mol25.960200oC+0.0426802000C2=18137J

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