## Chemical Engineering Thermodynamics - 2 - Dec 2015

### Chemical Engineering (Semester 5)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1(a)** Write short note on Thermodynamic equilibrium(5 marks)
**1(b)** Write short notes on Gibbs Duhem Equation.(5 marks)
**1(c)** Explain Vandervaal's equation.(5 marks)
**1(d)** Explain properties of refrigerants.(5 marks)
**2(a)** For binary solution the activity coefficient of component is $$ \ln \gamma_1=Ax_2^2$$ where A is constant. x_{2} is mole fraction of component 2. Obtain an expression for activity coefficient of component 2 in the same solution.(7 marks)
**2(b)** What azeotropic? What is the effect of pressure on the azeotropic composition?(6 marks)
**2(c)** Derive the relationship between the mole fraction of the components taking part in the reaction and the extent of the reaction.(7 marks)
**3(a)** Show that the fugacity of a gas obeying the vanderwaal's equation of state is given by: $$ \ln\ f=\dfrac{b}{v-b}-\dfrac{2a}{RTV}+ \ln\dfrac{RT}{V-b}$$(10 marks)
**3(b)** Describe the procedure to find the partial molar properties using the graphical method.(10 marks)
**4(a)** A gas mixture containing 25% CO, 55% H_{2} and 20% inert gas is to be used for methanol synthesis. The gases issue from the catalyst chamber in chemical equilibrium with respect to the reaction: CO_{(g)}+2H_{2(g)}→CH_{3}OH_{(g)} at pressure of 300 bar and temperature of 625K. Assume that the equilibrium mixture forms an ideal solution and k_{Ρ} and k_{Φ} are 4.9 × 10^{-3} and 0.35 respectively. What is the percent conversion of CO?(10 marks)
**4(b)** For a binary system of components A and B the activity coefficient are given by the relation lnγ_{1}=0.976x_{B}^{2}. The vapor phase data in bars are given by $$ \ln p_A^0=9.7321-\dfrac{2866.6}{t+217.88}; $$$$\ln p_A^0=12.0586-\dfrac{3667.7}{t+226.18}\ $$ is in °C. Does this system form an azeotropic at 71.7°C? If so at what composition?(10 marks)
**5(a)** A vapor compression refrigeration unit using Freon-12 operates between 151kpa and 746.6kpa. The fluid leaving the evaporator is saturated vapor and leaves the condenser at 303k. Calculate: (i) Refrigeration effect. (ii) Power required. (iii) COP. (iv) mass flow of refrigerant for refrigeration capacity of 4 Tons of refrigeration. Properties of Freon-12:

C_{p}=0.74 KJ/kgK

p_{s}kpa | T_{s} °k | V_{s}m^{3}/kg | H_{L}kJ/kg | H_{V}kJ/kg | Entropy kJ/kg°k |

151 | 253 | 0.1093 | 17.81 | 179.63 | 0.7123 |

746.6 | 303 | 0.0236 | 64.77 | 201.10 | 0.6903 |

**5(b)**What is standard heat of reaction and derive an expression for effect of temperature on standard heat of reaction?(8 marks)

### Attempt the following questions :

**6(a)** Explain vapor absorption refrigeration cycle with neat sketch(10 marks)
**6(b)** Explain various methods to determine thermodynamic critical properties with appropriate equations.(10 marks)