Tutorial-1

TUTE SHEET- 1
THERMODYNAMICS



1. Explain following with suitable examples.
Homogeneous and Heterogeneous system, Intensive and Extensive properties. Reversible and Irreversible process. Work, internal energy and heat, 1st law of thermodynamics. Also mention the units of DH, DS, q, w, E, DG, in SI and CGS systems.
2. Define enthalpy. Why is the enthalpy change, regarded as a measure of heat change involved in a process accruing at constant pressure?
3. Prove DH = qp; DH = DE +D ngRT; ­­-(DG) = Wmax; and –(DA) = Wmax - PDV
4. Define heat capacity.
5. Show that Cp – Cv = R
6. What do you understand by spontaneous process? Give some example.
7. Define entropy and discuss its physical significance.
8. Derive the expression for entropy change for an Ideal gas.
9. The enthalpy change for the transition of liquid water to steam DH vap is 40.8KJmol-1 at 1000C. Calculate the entropy change (DSvap) for the process. (Ans 109.38J/K.mol)
10. Two moles of an ideal gas expand isothermally and reversibly from a volume of 10 dm3 to 20dm3 at 300 K calculate the entropy change involved. (Ans. 11.53JK-1).
11. One mole of an ideal gas (monatomic) expands reversibly from a volume of 5dm3 to 10 dm3 and temperature 300K to a volume of 25dm3 and temperature 230K. Assuming that Cv = 3/2 R. Calculate DS for the process. (Ans. 4.305 JK-1 mol-1)
12. Calculate the change in entropy accompanying the heating of one mole of helium gas, assumed ideal, from a temperature 298K to a temperature at 1000K at constant pressure. Assume the Cv=3/2R (Ans. 25.17 JK-1mol-1)
13. One mole of an ideal gas heated from 100K to 300K. Calculate DS, if (i) the volume is kept constant (ii) the pressure is kept constant. Assume that Cv = 1.5R (Ans. 13.17 JK-1 ; 22.8JK-1 mol–1).
14. What do you understand by a spontaneous process and spontaneity of a process? Discuss the spontaneity of a process in terms of Gibbs free energy change.
15. What was the need to introduce the 2nd Law thermodynamics? State the law by five different ways & also give justification for 1st law of thermodynamics.
16. Show that decrease in change in free energy in a process is a measure of the maximum work (reversible work) done by the system.
17. Show that decrease in change in Helmholtz free energy function (work function) gives the max. work that can be obtained from a system during the change at constant temperature & pressure.
18. Derive the relation, dG = Vdp – sdT, ; ;
(DG)T = 2.303 nRT log and (DA)T = 2.303nRT log v1 / v2.
19. Derive Gibbs – Helmholtz equation in terms of free energy & in terms of work function also discuss its significance.
20. Derive Clapeyron – Clausius application in its integrated form with its applications. Under what conditions it is integrated.
21. The free energy change (DG) accompanying a given process is –85.77 kJ at 250C and –83.68 KJ at 350C. Calculate the change in enthalpy (DH) for the process at 300C. (Ans. DH = - 148.05 kJ).
22. Vapour pressure of water at 950C and 1000C are 634 and 760 mm, respectively. Calculate the molar heat of vaporization, DHv, of water between 950 and 1000C. (Ans. DH = 41363J/mol)
23. The vapour pressure of water at 1000C is 760mm. What will be the vapour pressure at 950C. The heat of vapouration water in this temperature range is 41.27 kJ per mole (Ans. P2 = 634.3mm).
24. DG for a reaction at 300K is – 16 Kcal, DH for the reaction is – 10Kcal. What is entropy of the reaction? What will be DG at 330K? (Ans. DS = 0.02 Kcal or 20 cal K-1; DG = 16.6 Kcal).
25. Calculate DH, DS, DG and DE when 1 mole of water is vaporized at 1000C and 1 atm. The latent heat of vaporization of water is 540 cal/g. (Ans. DS = 26.06; DG = 0; DE = 8979.5 Cal; DH = 9,720 Cal).
26. Define chemical potential and write the symbol of that and also explain the significance of chemical potential.
27. Compute the change in chemical potential of a substance if the partial pressure of a ideal gas falls from 1.00 atom to 0.5 atm at 298K (Ans. –1,717.3 J mil-1)
28. At what temperature will water boil when the atm. Pressure is 528mm Hg? Latent heat of vap. of water is 545.5 cal/g (Ans. 363K).
29. Show that entropy change for reversible process is zero and for irreversible process it is always positive (tends to be increasing).
30. Calculate the change in volume for melting of 1 g mole of phenol. Given latent heat of fusion = 3250 cal / g mol. Melting point of phenol = 330 K; dP / dT = 287atm /K.