  Question

# n kmol of a monochromatic ideal gas is taken quasi-statically from state A to state C along the straight line shown in the given figure. Alternatively, the same gas is shown in the  taken quasi-statically from A to C along the path ABC. Match the column (i) with column (ii) on the basis of the given information.  Column (I) Column (II) i. The heat ΔH added to  the gas along the straight line  path AC a.2PAVA ii. Change in  ΔU of the gas along the straight line path AC b. 132PAVA iii. The work done by the gas along the path ABC c. 6PAVA iv. The heat ΔH added to the gas along the path ABC d. 92PAVA    i→c; ii→d; iii→a; iv→bi→a; ii→c; iii→b; iv→di→b; ii→a; iii→c; iv→di→d; ii→a; iii→b; iv→c

Solution

## The correct option is A i→c; ii→d; iii→a; iv→b(i). Heat, ΔH added to the gas along the straight line path AC.       (a) Work ΔWAC   done by the gas along the straght line path AC               ΔWAC=(∫CAPdV)                            i.e., area under the path.        ΔWAC=PAVA+12PAVA=32PAVA     (b). Increase of internal energy is ΔUAC and, ΔUAC=32nRT(TC−TA)=32(PCVC−PAVA)=92PAVA   Hence, heat added,  ΔHAC=ΔWAC+ΔUAC=6PAVA (ii). From above, ΔUAC=92PAVA (iii).  Work done isΔWABC=ΔWAB+ΔWBC=0+PC(VC−VA)=2PAVA (iv). Heat ΔH added to the gas along ABC, ΔHABC=ΔHAB+ΔHBC=92PAVA+2PAVA=132PAVA  Suggest corrections   