real gas, the internal energy (Ans: a) (a) Increases with the increase in volume. (b) Decreases with the increase in volume.

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1 . When a gas s expanded adabatcally to a larger volume and a lower pressure the volume s smaller than t would be after an sothermal expanson under dentcal condtons. (Ans: rue). he statement corresponds to spontaneous and rreversble process. (Ans: False) 3. he entropy mxng equal volumes of the same deal gas at constant temperature and pressure wll be (Ans: zero) 4. ranslaton partton functon a molecule s an varable (Ans: extensve) 5. he nternal pressure U of an deal gas s zero. If attractons are domnant n a real gas the nternal energy (Ans: a) (a) Increases wth the ncrease n volume. (b) Decreases wth the ncrease n volume. 6. An adabatc process s (Ans: b) (a) Isoentalpc q d < (b) Isoentropc (c) sobarc (d) sochorc 7. onsder two reversble arnot engnes A and B. Engne A uses a real gas and engne B uses an deal gas. If the two engnes operate between the same temperature lmts and ( > ) then whch one s true? (Ans: c) (a) he effcency of A wll be greater than B. (b) he effcency of A wll be less than B. (c) he effcency of A wll be equal to B. (d) annot be predcted. 8. What are the maxmum number of phases that can be n equlbrum wth each other n a two component system? (Ans: c) (a) (b) 3 (c) 4 (d) 5 9. For whch of these processes s the value of negatve? (Ans: b) I. ugar s dssolved n water. II. team condenses on a surface. III. ao 3 s decomposed nto ao and O. (a) I only (b) II only (c) I and III only (d) II and III only

2 . Whch statement s correct about the substance represented by ths phase dagram? (Ans: d) (a) he sold sublmes at atm pressure. (b) Its normal bolng pont s above 3. (c) It exsts as a lqud at 8 and atm. (d) he densty of the sold s greater than that of the lqud.. 3. moles of an deal gas expands sothermally (n thermal contact wth the surroundngs; temperature 5 ) aganst a fxed external pressure of. bar. he ntal and fnal volumes of the gas are.l and 3.L respectvely. alculate change n the entropy of the system surroundngs and the unverse.

3 . What s the effcency a reversble engne operated around the cycle llustrated? (For step A to B consder the mean temperature of 5K) A (K) B 5 (J/K) 3. wo phases α and β of a pure substance exst n equlbrum at constant temperature and pressure. tartng from the fundamental equaton Gbbs energy prove that µ α µ β where µ s the chemcal potental. For two phases α and β at constant and the change n Gbbs free energy upon transferrng an nfntesmal amount of dn from α to β s gven by: ( dg) At equlbrum dg d + d + N s µ dn µ ( α) dn + µ ( β) dn dn [ µ ( β) µ ( α)] ( dg) dn [ ( β ) µ ( α)] µ

4 µ ( α) µ ( β ) (In ths partcular problem ) 4. alculate the pressure of O gas at 7K n the heterogeneous equlbrum reacton gven below f ths reacton s 3. kj mol -. ao 3( ) ao( ) + O ( g) Ans : K K O R ln( K p e R ) e 3J mol 8.34J K mol 7K A mxture of O(g) H (g) and H 3 OH(g) at 5K wth p(o) bar p(h ) bar and p(h 3 OH). bar s passed over a catalyst. Is ths reacton thermodynamcally feasble? Gven:. kj mol - and O( g bar) + H( g bar) H3OH( g.bar) Ans : p + R ln p.k J mol.7k J mol theree no methanol H3OH O ph +.834k J mol s postve hence the reacton wll be s med!. 5K ln not possble and

5 6. Usng the Maxwell s relatons obtaned from the basc thermodynamc relatons dhd+d and dgd-d and cyclc rule show that an deal gas nr d d dh From get we n ubsttutng relaton s Maxwell the derve can one d d dh from Now get we n ubsttutng d d have We rule cyclc the g U + (3) () ' () () () sn

6 ubsttutng We have nr nr ubsttutng n (4) we nr (4) get 7. he standard reacton Enthalpy of Zn(s) + H O(g) ZnO(s) +H (g) s approxmately constant at +4kJmol - from 9K up to 8K. he standard reacton Gbbs energy s +33kJ mol - at 8K. Estmate the temperature at whch the equlbrum constant becomes. Ans : rg ln K(8K) R K We have ln K We hs s the crosss over temperature. Now.45 want a keepng R ln K + H r 5K ln K temperature ln K 33J mol (8.34JK mol ) 8K r H R and an t Hoff s equaton ( ' ' ) that corresponds to ln K ln(). solvng 8.34JK mol ln(.45) + 4Jmol 8 K

7 8. N partcles are dstrbuted among three states havng energes E E k and E 3 k. If the total energy of the system s k what s the value of N?