Nr-220802-Chemical Engineering Thermodynamics - i

Set No:

1

Code No:220802 II.B.Tech II-Semester. Supplementary Examinations. January,2003 CHEMICAL ENGINEERING THERMODYNAMICS (Chemical Engineering) Time: 3 hours. Max.Marks:80 Answer any FIVE questions All questions carry equal marks. --1. Explain the following and give two examples of each a) (i) Extensive and Intensive properties. (ii) Reversible and irreversible processes. (iii) State function and path function. b) Water flows through a horizontal coil heated from the outside by high temperature flue gases. As it passes through the coil, the water changes state from 2 atm (202.66 KPa) and 180o F (82.2oC) to 1 atm (101.33 KPa) and 250o F (121.1oC). Its entering velocity is 10 ft/sec (3.05 m/s) and its exit velocity is 600 ft/s (182.9 m/s) Determine the heat transferred through the coil per unit mass of water. Enthalpies of the inlet and outlet water streams are inlet = 148 Btu/lbm (344.2 KJ/kg) output = 1168.8 Btu/lbm (2718.5 KJ/kg) 2. a) Explain the application of cubic equations of state. b) Determine the molar volume of n-butane at 510oK and 25 bar by each of the following. (i) The ideal gas equation (ii) The generalized compressibility factor correlation (iii) The generalized virial - coefficient correlation. 3. a) If 10 moles of ethylene is heated from 200oC to 1000oC in a steady flow process at approximately atmospheric pressure. What is its entropy change. Give that, A = 1.424; B = 14.394 x 10-3; C = -4.392 x 10-6; D = 0. b) One mole of an ideal gas is compressed isothermally but irreversibly at 400 K from 3 bar to 7 bar in a piston cylinder device. The work required is 35% greater than the work of irreversible isothermal compression. The heat transferred from the gas during compression flows to a heat reservoir at 300 K. Calculate the entropy changes of gas, reservoir and ∆ S total. 4. a) For acetone at 20oC and 1 bar β = 1.487x10-3 / 0C , K = 62X10-6/bar,

cm 3 V = 1.287 Find (i) gm (ii) (iii)

 ∂P    ∂T  v

The value of 

The pressure generated when acetone is heated at constant volume from 20oC and 1 bar to 30oC. The volume change when acetone is changed from 20oC and 1 bar to 0oC and 10 bar Contd…….2

Code No:220802 b)

-2-

Set No:1

Show that (i)

 T   ∂V  2 V  ∂V   ∂V   ∂V        =  +   − ∂ P ∂ P C  H  T  p   ∂T  P C P  ∂T  P

(ii)

Cv P   ∂A   − S   =  ∂T  s T (∂P / OT  v

5. a) Derive Maxwell’s equations, explain their importance. b) Estimate VR, HR and SR for steam at 200oC and 1400 kpa by using generalized correlations. Given that TC = 647.3 K, PC = 220.5 bar, VC = 56 cm3/mol W = 0.344. 6.

Calculate Z and V for methanol vapour at 200oC and 10 bar by the following equations. a) A truncated virial equation Z =

PV B C = 1 + + 2 with the following values of RT V V

virial coefficients, B = -219 cm3/mol, C = -17,300 cm6/mol. b) The truncated virial equation Z =

PV BP with a value of B from the =1+ RT RT

generalized pidzer correlation. c) The Red lich -Kwong equation with estimates of a and b given, Tc = 512.6K, Pc = 81 bar W = 0.564.

7. a) Explain about the variations of heat capacity of a substance with temperature. b) How much heat would be absorbed or released from hydrogenation of acetylene to ethane at standard conditions. C2 H2 (g) + 2H2 (g) C2 H6(g) (i) Use heat of combustion data (ii) Use heat of formation data. Combustion data at 25oC : C2 H2 : ∆HoC = -310620 cal/gm C2 H6 : ∆HoC = -372820 cal/gm H2 : ∆HoC = -68317 cal/gm Heat of formation data at 25oC: C2 H2 : ∆Hƒ = 54194 cal/g.mole C2 H6 : ∆Hƒ = -20236 cal/g.mole 8.

Write short notes on any two of the following. (i) Phase rule and criterion for equilibrium. (ii) Heat effects of Industrial reactions. (iii) Thermodynamic properties of an ideal bas. @@@@@

Set No:

2

Code No:220802 II.B.Tech II-Semester. Supplementary Examinations. January,2003 CHEMICAL ENGINEERING THERMODYNAMICS (Chemical Engineering) Time: 3 hours. Max.Marks:80 Answer any FIVE questions All questions carry equal marks. --1. a) State the first law of thermodynamics. Obtain an expression for first law of thermodynamics for a steady state flow process. b) A particular substance undergoes a mechanically reversible process, expanding from an initial state of 20 bar to final state of 8 bar. The path for the process is described by the equation P =

0.036 − 4 where P is in bar and Vt is in m3. t V

( )

If ∆V t for the change of state is -1400J, determine W, a and ∆H t . Air is compressed from an initial condition of 1 bar and 25oC to a final state of 5 bar and 25oC by three different mechanically reversible processes. (a) Heating at constant volume followed by cooling at constant pressure. (b) Isothermal compression. ( c) Adiabatic compression followed by cooling at constant volume. At these conditions air may be considered as an ideal gas with the constant heat capacities

2.

 5  2

7  2

Cv =   R and CP =   R. Calculate the work required, heat transferred and the changes in the internal energy and enthalpy of air for each process. 3.

Calculate the molar volume of saturated liquid and the molar volume of saturated vapor by the Redlich Kwong equation for the propose at 40o C where Psat = 13.7 bar. Given that, TC = 369.8K, PC = 42.5 bar, W = 0.152, VC = 203 cm3/mol, ZC = 0.281.

4.a) b)

What are the different statements of second law of thermodynamics. Show that the efficiency of an irreversible heat engine is always than of a reversible heat engine. One kilogram of water at the constant pressure of 1 atm, raised from 25oC to the boiling point and then completely vapourized at this pressure. What is the entropy change of the given process. Latent heat of vaporization at 1 atm is kJ 2257 kJ/kg, CP = 4.184 kgK Contd……2

Code No:220802 5.

-2-

Set No:2

Show that (i)



 ∂V     dP and  ∂T  P 

dH = CP dT + U − T 



  ∂P  

 

− P  dV dv = CV dt + T  ∂T (iii)

 UP  CP-CV = - T    UT V

2

 UV     UT  P

6.

If heat in the amount of 13,00 KJ is added to 40 mol of SO2 initially at 4000C in a steady state flow process at approximately atmospheric pressure, what is its entropy change. For SO2 : A = 5.699, B = 0.801 x 103, C = 0, D = -1.015x10-5

7.

A particular power plant operates with the heat source reservoir at 3000C and a heat sink reservoir at 250C, it has a thermal efficiency equal to 60% of the carnot engine thermal efficiency for the same temperature. What is the thermal efficiency of the plant To what temperature must the heat source reservoir be raised to increase the thermal efficiency of plant to 40%, again efficiency is 60% of cannot engine value .

a) b)

8.

Answer any TWO of the following: a) State the difference between state function and path function with examples. b) Enumerate the characteristics of a reversible process. c) What is the final temperature when 0.4x106 (Btu) are added to 25 (lb mol) 8 ammonia initially at (5000F) in a steady flow process at 1 atm. Data: A = 3.578, B = 3.020x10-3, C = 0 , D = -0.186 x 105. ********

Set No: Code No:220802 II.B.Tech II-Semester. Supplementary Examinations. January,2003 CHEMICAL ENGINEERING THERMODYNAMICS (Chemical Engineering) Time: 3 hours. Max.Marks:80 Answer any FIVE questions All questions carry equal marks. --1.a) Distinguish between state function and path function. b) Distinguish between a reversible process and an irreversible process. c)

 

A certain gas obeys the relation  P +

3

a   (V-b) = RT where a,b and R are V2

constants. Derive a relation for the work done by the gas when it changes from V1, T to V2, T. 2.a) b) 3.a) b)

State the first law of thermodynamics. Derive an expression for first law of thermodynamics for a steady-state flow process. For one mole of an ideal gas undergoing reversible adiabatic process, show that PVr = constant. Where r = CP/Cv. One kilo mole of methane is stored in a 0.3m3 tank at 300 0K. Estimate the pressure of the gas using ideal gas law and Redlich-Kwong equation of state. TC = 190.6 oK PC = 4.6 MPa State Two parameter and three parameter law of corresponding states. Explain Pitzer’s modification to law of corresponding states.

4.a) What do you mean by criterion of Exactness? Using criterion of Exactness derive the four Maxwell relations. b) Consider S=S(T,P) and S=S(T,V) and derive the following relations: (i) T ds = Cp dT - βVΤ dp (ii) 5.a)

T ds = CV dT +

Tβ dV K

A Turbine in a steam power plant operating under steady state receives 1 kg/s super heated steam at 3.0 MPa and 3000C. The steam enters the turbine with a velocity of 10 m/s at an elevation of 5 m above the ground level. The Turbine discharges wet steam 50 KPa pressure with a velocity of 50 m/s at an elevation of 10m above the ground level. The energy losses as heat from the Turbine casing are estimated to be 10 KJ/s. Estimate the power output of the Turbine. kJ Enthalpy of super heated steam at 3 MPa and 300oC = 2993.5 kg Enthalpy of wet steam at 50 kPa = 2300.08 kJ/kg. Contd….2

Code No;220802 -2Set No:3 b) An ideal gas (r=1.4) at 0.1 MPa and 300 oK enters an adiabatic compressor at the rate of 1 mol/s and leves at 750 oK. Calculate the power consumed by the compressor. 6.a) A reversible heat engine A absorbs energy from a reservoir at T 1 and rejects energy to a reservoir at T2. A second reversible engine B absorbs the same amount of energy as rejected by the engine A from the reservoir at T 2 and rejects energy to a reservoir at T3. What is the relation between T1, T2 and T3 if: (i) The efficiencies of engines A and B are same. (ii) The work delivered by the engines are same One mole of Nitrogen Cr=1.4) at 0.1 MPa and 300 oK. has been subjected to a series of processes as a result of which it reached the state P=0.5 MPa and 600 0K Determine the change in Entropy of Nitrogen. Nitrogen may be treated as an ideal gas. 7.a) An insulated and rigid container is divided into two compartments. care compartment contains 2 kmol Melium at 1.0 MPa and 600 0K, while the second compartment contains 5 Kmol air at 2.0 MPa and 500 0K. The partition is punctured and the gases are allowed to mix. Calculate the entropy change associated with this process. Helium and air may be treated as ideal gases. CV(He) = 1.5 R kJ/Kmol - 0K and CV(air) = 2.5 R kJ|kmol- 0K. b) Explain phase rule with suitable examples. 8.a)

Calculate the standard heat of the following reaction at 1000 0K. 2 SO2 (g) + O2 (g) → 2 SO3 (g) Data: CP0 (SO2) = 47.38 x 10-3 + 6.66x10-6 T CP0 (SO3) = 67.01 x 10-3 + 8.78x10-6 T CP0 (O2) = 30.25 x 10-3 + 4.21x10-6 T

b)

Where CPo denotes the molar heat capacity in the ideal gas state and is given in kJ/mole - 0K. Take ∆ H0f 298 = - 197.78 kJ. Define: (i) Standard heat of reaction (ii) Standard heat of formation. *********

Set No: Code No:220802 II.B.Tech II-Semester. Supplementary Examinations. January,2003 CHEMICAL ENGINEERING THERMODYNAMICS (Chemical Engineering) Time: 3 hours. Max.Marks:80 Answer any FIVE questions All questions carry equal marks. -1.a) Define the following terms: (i) Enthalpy (ii) Internal energy (iii) Gibbs energy (iv) Helmholtz free energy b) Explain phase rule. Give suitable examples. c) Distinguish between state function and path function. d) State Zero’th law of thermodynamics. e) Distinguish between closed system and open system 2.a) b) c)

4

Heat in the amount of 5 kJ is added to a system while its internal energy decreases by 10 kJ. How much energy is transferred as work? For a process causing the same change of state but for which work is zero how much heat is transferred? What do you mean by an intensive property and extensive property. State the first law of thermodynamics. Derive an expression for first law of thermodynamics for a steady state flow process.

5R 3R and CV = is changed from P1 = 1 bar and V1 = 10 m3 2 2

3.

An ideal gas CP =

4.a)

to P2 = 10 bar and V2 = 1 m3 by the following mechanically reversible processes: a) Isothermal compression b) Adiabatic compression followed by cooling at constant pressure. c) Adiabatic compression followed by cooling at constant volume d) Heating at constant volume followed by cooling at constant pressure calculate Q,W, ∆U , ∆H for each of these processes. Show that the vander waals constants a and b are given by : 2 2 RTC a = 27 R T C and b =

64 PC

8PC

b) What is a cubic equation of state ? Give few examples for cubic equations of state. c) An empirical equation, PV = constant, where δ is a constant B sametimes used to relate P and V for any mechanically reversible process. Assuming the validity of this equation for an ideal gas, show that: δ −1    P2  δ   RT1 1−  ω   P1   δ − 1   =

Contd……..2

Code No:220802 5.a) b)

-2-

Set No:4

Starting from Fundamentals, derive the four Maxwell relations. (i) Consider h = h (T,P) and derive the following relation: dh =CP dT + V (1-T β ) dp (ii) Consider u = u (T,V) and show that :

 Tβ  − P  dv  K 

du = CV dT +  6.a) b)

c)

Derive the clausius clapeyron equation and write down the assumptions involved in it. An insulated container has 1 kg super cooled liquid water at -100C. Suppose a negligible amount of ice is added as a seed to aid solidification. Calculate the mass of water which solidifies and the change in Entropy associated with the process CP of water is 4.2 kJ/kg - 0K and the latent heat of fusion of water at 00C is 333.43 kJ/kg. A carnot Engine I operates between two reservoirs at Temperatures 2000 0K and T , while carnot Engine II operates between the reservoirs at T and 300 0K. If is found that both the Engines have the same efficiency. Determine the value of T.

7.a) b)

Explain the Thermodynamic analysis of a Nozzle Saturated steam at 175 KPa is compressed adiabatically in a centrifugal compressor to 650 KPa at the rate of 1.5 kg/s. The compressor efficiency is 75%. What is the power requirement of the compressor and what are the Enthalpy and Entropy of the steam in its final state?

8.

Calculate the Theoretical Flame temperature when methane at 250C is burned with 50%. Excess air preheated to 5000C. Date: i A Bx103 Cx106 Dx10-5 ∆ Hf,J/mole O2 3.639 0.506 0.0 -0.227 ----N2 3.280 0.593 0.0 0.040 ----CH4 1.702 9.081 -2.164 0.0 -74520 CO2 5.457 1.045 0.0 -1.157 -393509 H2O(g) 3.47 1.45 0.0 0.121 -241818 *********