**Anna University, B.Tech Chemical Engineering, V – Semester**

**Chemical Engineering Thermodynamics I**

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**PART A** **(10 X 2 = 20 Marks)**

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1. What are point and path properties? Explain with examples.

2. Explain the term “energy content” of a system.

3. Bring out the differences between reversible and irreversible processes.

4. Explain briefly the limitations of first law of thermodynamics

5. Explain the term “heat Capacity”. What do you understand by C_{P} and C_{v.}

6. State and explain the second law of thermodynamics.

7. What is an equation of state? Explain with an example.

8. Define fugacity and fugacity coefficient?

9. What is the effect of clearance volume on compression? Explain with the help of a P-V diagram.

10. Explain the terms:

(a) Convergent – divergent flow and

(b) Constant throat velocity

**PART B ** **(10 X 2 = 20 Marks)**

11. Prove the following:

(a) ?T = – ?p

?? s ?S v

(b) [Cp/ C? ] = – ?? ?T ?p

?T _{p} ?p _{v } ?? _{s}

(c) [ ?U/ ?? ] T = – { p + T (?? / ?T)_{p/} (?? / ?p)_{T }}

_{ }

12. (a) An ideal gas (C_{p} = 5 and C? = 3 cal/gm mole ? K)is at 1 atm has a volume and of

V_{1} = 22.4 m^{3}. It is brought to P_{2 }= 10 atm and V_{2} = 2.24 m^{3} by the following

reversible processes.

(i) Isothermal compression.

(ii) Adiabatic compression followed by cooling at constant pressure.

(iii) Heating at constant volume followed by cooling at constant pressure. Calculate ?,?, ? U and ? H for each step of this overall process.

OR

(b) A pressure cylinder contains 50 litres of nitrogen weighing 400 grams. What is the maximum temperature to which the cylinder could be exposed, if the pressure in the cylinder should not exceed 80 atmospheres absolute? The compressibility factor at the above conditions for nitrogen is 0.946.

R = 82.1 (cc) (atm)/ (gm mole) ? K.

13. (a) Derive an expression for the critical pressure and temperature ratio for flow of an ideal gas thro a nozzle.

### OR

(b) (i) Deduce the expressions giving the effect of pressure and temperature on fugacity of component i in a solution.

(ii) Show that the fugacity of a gas obeying the equation of state p(v – B) = RT, is given by

f = pe^{Bp}/ ^{RT}

14. (a) Calculate the total change in entropy for the following processes.

(i) one gram of an ideal gas cp = 7 cal / gm mole ? K is cooled at 10 atm abs. Pressure from 500 ? K to 300? K and then expanded isothermally to 1atm.abs. pressure and 300 ? K.

(ii) 100 grams of lead shot C_{p} = 0.03 cal/gm? C initially at 300? C is mixed

adiabatically with 100 grams of water at 30? C.

OR

(b) A three stage reciprocating flow compressor is designed to compress 800 litres of

oxygen per minute at 30? C from 1 atm. Abs. Pressure to 100 atm.abs.pressure.

inter cooling at every stage is done at 30 ? C. Calculate the theoretical work in

litre-atmosphere per minute required for reversible adiabatic compression of the

gas, taking that the gas is ideal. What should be the discharge pressure for each

stage c_{p} / c_{v} = 1.4 for this gas.

15. (a) show how to calculate the constants a and b in the Berthelot equation of state:

P = RT/ V-B – a/TV^{2}

for any substance by applying only the conditions at the critical point.

## OR

(b) Prove that the work of an adiabatic process involving an ideal gas is given by

W = {RT_{1/ r – 1}} { 1 – [P_{2/P1]} ^{r-1/ r}}

Show also that this equation, for an isothermal process for which r = 1 reduces to

W = RT ln P_{1/ }P_{2}

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