The work done by a mass less piston in causing an expansion $∆$V (at constant temperature), when the opposing pressure, P is variable, is given by:

1. W= $-\int \mathrm{P}∆\mathrm{V}$               

2. W=0

3. W= -P$∆$V                     

4. none of these

Entropy decreases during:

1. crystallization of sucrose from solution

2. rusting of iron

3. melting of ice

4. vaporization of camphor

Entropy change of vaporization at constant pressure is given by:

1. $∆{\mathrm{S}}_{\mathit{(p}\mathit{)}}= \frac{∆{\mathrm{Hp}}_{}}{\mathrm{T}}$

2. $∆{\mathrm{S}}_{\mathit{\left(}v\mathit{\right)}}=\frac{∆{\mathrm{U}}_v}{\mathrm{T}}$

3. $∆{\mathrm{S}}_{\mathit{\left(}v\mathit{\right)}}= \frac{∆{\mathrm{H}}_v}{\mathrm{P}}$

4. None of the above

What is the entropy change for the reaction given below, 

2H₂ (g) + O₂ (g) $\to$2H₂O(l)

at temperature 300 K? Standard entropies of H₂ (g), O₂(g) and H₂O(l) are 126.6, 201.20 and 68.0 JK^-1mol^-1 respectively.

1. -318.4 JK^-1mol^-1                           .

2. 318.4 JK^-1mol^-1 

3. 31.84 JK^-1mol^-1                             

4. none of these

If S$°$ for H₂, Cl₂ and HCl are 0.13, 0.22 and 0.19 kJ K^-1mol^-1 respectively. The total change in standard entropy for the reaction, H₂ + Cl₂ $\to$2HCl is:

1. 30 J K^-1mol^-1                         

2. 40 J K^-1mol^-1

3. 60 J K^-1mol^-1                         

4. 20 J K^-1mol^-1

The direct conversion of A to B is difficult and thus it is converted by path A$\to$C$\to$D$\to$B. Given

$∆{\mathrm{S}}_{\mathrm{A}\to \mathrm{C}}=50 \mathrm{e}.\mathrm{u}; ∆{\mathrm{S}}_{\mathrm{C}\to \mathrm{D}}=30 \mathrm{e}.\mathrm{u}; ∆{\mathrm{S}}_{\mathrm{B}\to \mathrm{D}}=20 \mathrm{e}.\mathrm{u}.$

(Where e.u. is the entropy unit)
then $∆{\mathrm{S}}_{\mathrm{A}\to \mathrm{B}}$ would be:

1. +60 e.u                                       

2. +100 e.u

3. -60 e.u                                       

4. -100 e.u

In a flask, colourless N₂O₄(g) is in equilibrium with brown coloured NO₂(g). At equilibrium when the flask is heated to 100$°$C, the brown colour deepens and on cooling it becomes less coloured. Which statement is incorrect about this observation?

1. The $∆$H for the reaction N₂O₄(g)$\rightleftharpoons$ 2NO₂(g) is +ve

2. Paramagnetism increases on heating

3. The $∆$H-$∆$U at 100$°$C is equal to 200 cal

4. Dimerisation is reduced on heating

Enthalpy of the reaction,

CH₄(g) + 1/2O₂(g) $\to$CH₃OH(l), is negative. If the enthalpy of combustion of CH₄ and CH₃OH are x and y respectively, then
which relation is correct?                                 

1. x>y         

2. x<y         

3. x=y           

4. x$⩾$y

In the reaction, $∆$H and $∆$S both are positive. The condition under which the reaction would not be spontaneous is -

1. $∆$H>T$∆$S                             

2. $∆$S=$∆$H/T

3. $∆$H=T$∆$S                               

4. All of the above

When an ideal gas is compressed adiabatically and reversibly, the final temperature is:

1. higher than the initial temperature

2. lower than the initial temperature

3. the same as the initial temperature

4. dependent on the rate of compression