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SURNAME: ________________________ 2nd Semester AY 13-14. MAFabro. MetE 17 First Long Exam

Metallurgical Thermodynamics

First Long Examination

11 January 2014

DIRECTIONS:

1.  Make sure that each page has your name and student number at

the top portion of the paper.2.  Use only blue or black ink.

3.  Show your complete solution (working equation, substitution of

values with units, sub-steps and final answer). Intermediate values

that must be solved but are not explicitly asked for may only be

underlined twice. Express your final answers up to three decimal

places and enclose in a box.

4.  Write clearly and legibly. Illegible and messy solutions will not be

given partial points.

5.  Start each exam section on a new page. You may write on the

back pages.

6.  Mobile phones and other electronic devices must be put to silent

mode or turned off, and left inside your bag.

7.  Only the proctor or instructor may be asked if you have questions

or clarifications.

8.  Any student caught cheating will be given a grade of zero for this

exam, and will be reported to the Dean’s Office and the Student

Disciplinary Tribunal.

Section 1 - EASY: Answer the following problems. Any points obtained

beyond 25 will be considered bonus points for this exam.

1.  Derive the universal gas constant from the combinations of the

equations of state of ideal gases. (5 points)

2.  Show that at relatively low temperatures, the enthalpy of formation

of pyrite (FeS2) is higher that that of gold by using the Dulong-Petit

and Kopp-Neumann methods of estimation. (10 points)

3.  Given that constant temperature processes do not have a change

in internal energy, derive from the first law of thermodynamics the

equation that governs the behaviour of gases under

•  Isothermal conditions (5 points) 

•  Isochoric conditions(5 points) 4.  Demonstrate that work is path dependent. (5 points)

Section 2 - MODERATE PROBLEM

A particular pressure filter, shown in the diagram below, dewaters pulpby using an elevated pressure to push water through a settled bed of

solids and the filter paper. It is operated thus:

•  Pulp (a mixture of water and solids) is poured into the cylinder  

•  A leak proof lid with gasket is fitted on top of the cylinder 

•  Compressed gas is fed into the

cylinder until a certain pressure is

reached, after which the valve is

closed, cutting off the gas inside the

cylinder from the compressed gas

source and the surroundings. 

• 

Water is forced through the settledbed of solids and filter paper, exits

through the water outlet, eventually

leaving behind a significantly

dewatered layer of solids called a

filter cake. 

Consider a cylinder with an inside

diameter of 24 cm and a height of 36

cm, set in a laboratory at 30!. Pulp

is poured into the cylinder until 8 cm is left between the pulp surface

and the brim. The lid is fitted and latched. Compressed diatomic, idealgas is pumped into the cylinder until a pressure of 5.155 atm is

reached. The valve is closed. It was observed that water was

discharged at a constant rate of 0.013572 L per second.

1.  Express the volume occupied by the ideal diatomic gas as a

function of time t  in seconds.

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SURNAME: ________________________ 2nd Semester AY 13-14. MAFabro. MetE 17 First Long Exam

2.  Express the pressure (atm) of the ideal diatomic gas as a function

of time t  in seconds.

3.  Assume that there is no heat transfer between the gas and the

pulp. Find the pressure and temperature of the gas after 15

minutes, the work done by/on the gas, heat flow and change in

internal energy of the gas for the following conditions:

1. 

The cylinder, lid and base is made of a strong metal; and2.  The cylinder, lid and base is made of Aerogel, a perfectly

insulating material.

4.  Assume now that thermodynamic equilibrium is allowed to exist

between the remaining pulp and the gas. Which pressure filter is

more convenient (or less problematic) to use, the one made of

metal, or Aerogel? Why?

Section 3 - DIFFICULT PROBLEM

Octane is an alkane with a chemical formula C8H18. Octane and its

many isomers are very flammable and are components of gasoline.

A combustion chamber, lined with insulating refractory bricks, is filled

with 0.3 mole of octane and stoichiometric air. If the combustion of

octane is allowed to proceed at 500 K,

1.  How much energy is produced when the octane supplied is

completely consumed?

2.  How much dry air must be provided for the octane to combust

completely?

3.  How much of each gas is present in the chamber after octane is

consumed?

4.  A 5.23272 kg of solid Zn specimen was placed in a refractory

container, left inside the combustion chamber and was in thermal

equilibrium with the gases in the combustion chamber. The

combustion of octane cause the entire contents of the chamber to

reach 809.52 K, including the zinc sample, which was found to be

completely molten. Determine the melting point of zinc.

5.  What is the minimum amount of excess air (expressed in

percentage relative to stoichiometric amount) must be supplied to

keep the zinc sample from melting?

Hf298 (C 8H18) = -250.3 kJ/mol

Boiling point of C8H18 : 398.75 K

Latent heat of vaporisation of octane: 8137.83 cal/mol

Cp (C 8H18)(l)  = 61.10752 cal/mol-K

Cp (C 8H18)(g)  = -1.7459 x 10-4 T 2 + 0.5567 T + 51.38225 J/mol-K

Latent heat of fusion of Zn: 1766 cal/mol

R = 0.082057 L-atm/mol-k or 8.314 J/mol-K

1 joule = 0.239 calories

C : 12.01

H : 1.01

O : 16

N : 14.01

Zn : 65.41