Gujarat Technological University 2010-3rd Sem B.Tech Biotechnology Thermodynamics - Question Paper
Seat No. Enrolment No.
GUJARAT TECHNOLOGICAL UNIVERSITY
B.E. Sem-III Regular / Remedial Examination December 2010
Subject Name: THERMODYNAMICS Date: 18 /12 /2010 Time: 10.30 am - 01.00 pm
Total Marks: 70
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. All the Notations bear their conventional meanings.
Q.1 (a) Define Thermodynamics, system, surrounding, state and process. Also, mention 07 various statements of zeroth, first, second and third law of thermodynamics.
(b) Air at 1 bar and 298.15 K (25oC) is compressed to 5 bar and 298.15 K by two 07 mechanically reversible processes:
i) Cooling at constant pressure followed by heating at constant volume.
ii) Heating at constant volume followed by cooling at constant pressure.
Calculate the heat and work requirements and A U and A H of the air for each path.
The following heat capacities for air may be assumed independent of temperature:
Cv = 20.78 and Cp = 29.10 J mol-1 K-1
Also assume for air that PV/T is a constant, regardless of the changes it undergoes.
At 298.15 K and 1 bar the molar volume of air is 0.02479 m3 mol-1.
Q.2 (a) What is the final temperature when heat in the amount of 930 kJ is added to 25 07 moles of ammonia initially at 260oC in a steady-flow process at approximately 1 atm?
Cpig/R = 1.702 + 9.081 x 10-3 T - 2.164 x 10-6 T2 J/(mol K), T is in K
(b) Express the volume expansivity and the isothermal compressibility as functions of 07 density p and its partial derivatives. For water at 50 C and 1 bar, k =
44.18 x 10"6 bar-1. To what pressure must water be compressed at 50C to change its density by 1 percent? Assume that k is independent of P.
OR
(b) Liquid/Vapour saturation pressure Psat is often represented as a function of 07 temperature by an equation of the form:
Log10 Psat (torr) = a - b
t(oC) + c
Here, parameters a, b and c are substance-specific constants. Suppose it is required to represent Psat by the equivalent equation:
ln Psat (kPa) = A -
T(K) + C
Show how the parameters in the two equations are related.
Q.3 (a) For steady flow in a heat exchanger at approximately atmospheric pressure, what is 05 the amount of heat required when 10 moles of SO2 is heated from 200oC to 1100oC? Heat capacity of SO2 is given by:
Cpig/R = 5.699 + 0.801 x 10-3T - 1.015 x 105T-2 J/(mol. K) , T is in K
(b) The turbines in a hydroelectric plant are fed by water falling from a 50 m height. 05 Assuming 91% efficiency for conversion of potential to electrical energy, and 8% loss of the resulting power in transmission, what is the mass flow rate of water required to power a 200 W light bulb?
(c) If the heat capacity of a substance is correctly represented by an equation of the 04 form, Cp = A + BT + CT2, show that the error resulting when <Cp>H is assumed equal to Cp evaluated at the arithmetic mean of the initial and final temperatures is C(T2 - Ti) 2 / 12.
OR
Q.3 (a) Derive a mathematical expression of the first law of thermodynamics for a closed 07 system with modern sign conventions. Define and explain internal energy and enthalpy.
(b) Explain Raoults law. At 303 K the vapour pressures of benzene (1) and toluene (2) 07 are 15.75 kPa and 4.89 kPa respectively. Assuming the validity of Raoults law, determine the partial pressure and composition of the benzene vapour in equilibrium with a liquid mixture consisting of equal weight of the two components.
(a) Derive the formulae for PVT relations, AU, W, Q and AH for Isothermal, Isobaric, 07 and Isochoric reversible processes for 1 mole of an ideal gas.
Q.4
(b) A piston/cylinder device contains 5 mol of an ideal gas, Cp = (5/2) R, and Cv = 07 (3/2) R, at 20C and 1 bar. The gas is compressed reversibly and adiabatically to 10 bar, where the position is locked in position. The cylinder is then brought into thermal contact with a heat reservoir at 20C, and heat transfer continuous until the gas also reaches this temperature. Determine the entropy change of the gas, the reservoir and ASTotal.
OR
(a) Explain the concept of entropy change in detail. 07
Q.4
(I) Ideal gas equation.
(II) Van der walls equation of state.
Critical constants of ethylene are 282.3 K and 50.4 bar.
Discuss fundamentals of chemical reaction equilibria with examples. 05
Q.5
(a)
(b)
(c)
Derive equation of COP (Coefficient of performance) of carnot refrigerator with 05 neat sketch.
Write a short note on thermodynamics diagrams. 04
OR
A mercury manometer used to measure pressure inside a vessel indicates 400 mm. 05 One end of the manometer is exposed to the atmosphere. The atmospheric pressure is 1.01325 bar. Density of mercury is 13.56 x 103 kg/m3 and g = 9.81 m/s2.
Q.5 (a)
What is the absolute pressure in the vessel in N/m2?
(b) An electric current of 0.5 A from a 12 V supply is passed for 5 minutes through a 05 resistance in thermal contact with saturated water at 1 atm. As a result, 0.798 g of water is vaporized. Assuming that the water vapour behaves ideally, calculate the molar internal energy change and enthalpy change during the process.
(c) For the two-phase systems, derive the Clausius / Clapeyron equation relating latent 04 heat of vapourization directly to the vapour-pressure curve.
2
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