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Thermodynamics

`2^(nd )`

law and application State Kelvin-Planck and Clausius statement for second law of thermodynamics and show that they are equivalent. Consider Carnot cycle and deduce

`w,q,\Delta U,\Delta H`

for each step. Show that

`\eta =1-(T_(L))/(T_(H))`

, where

`\eta `

is the efficiency and

`T_(L)&T_(H)`

are low and high temperature respectively. Hence define entropy and also evaluate entropy for each step of Carnot cycle. Write down the mathematical expression of

`2^(nd )`

law of thermodynamics. Hence get the criteria for spontaneity and equilibrium for a. Isolated system b. System at constant temperature and volume c. System at constant temperature and pressure What is the physical significance of

`\Delta A&\Delta G`

Get the expression of entropy for ideal gas in terms of (T,P) and (T,V) Draw the adiabatic, isochoric, isothermal and adiabatic process on T-S diagram. Show that

`\Delta G_(0)=-RTlnK_(P)`

. Also comment on the dependency of

`K_(P)`

on pressure and temperature.

`N_(2)O_(4)(g)⇄2NO_(2)(g)`

If at

`1atm`

pressure the degree of dissociation for the reaction is 0.533 , calculate the

`K_(p)`

`HgO(s)⇄Hg(l)+(1)/(2)O_(2)(g)`

Calculate the equilibrium pressure for

`O_(2)`

at

`298K`

if the change in Gibb's free energy is

`58.56k(J)/(m)ol`

For a reaction at

`700K`

, the equilibrium constant has the magnitude

`2\times 10^(-4)`

. What would be the value of Gibb's free energy if the stoichiometric coefficients are halved? In the gaseous reaction

`2A+B⇄A_(2)B`

, the change in Gibb's free energy

`(\Delta G_(0))`

is

`1200Cal`

. What would be the total pressure required to produce

`60%`

conversion of

`B`

into product when the initial molar ratio of

`A:B`

is

`2:1`

.[Given :

`R=1.987CalK^(-1)mol^(-1)`

] A ideal gas isothermally reversibly expands from volume

`V_(1)`

to

`V_(2)`

at

`500K`

temperature, where

`400J`

energy is absorbed during the process. Get the entropy change and workdone of the system. What would be the entropy change and the workdone of the system if the process is carried out isothermally but irreversibly from

`V_(1)`

to

`V_(2)`

at

`500K`

, where

`200J`

heat is being absorbed. 0.5 mole of ideal gas at

`0\deg C`

is allowed to expand reversibly isothermally to 10 times of its initial volume. Calculate

`w,q,\Delta U,\Delta H,\Delta S,\Delta G`

. What would be the values if the process is irreversible. [given: initial pressure is

`5atm`

]