${∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$ of formation of ${\mathrm{CH}}_4\left(\mathrm{g}\right)$ at certain temperature is $-393$ $\mathrm{kJ}$ ${\mathrm{mol}}^{-1}$. The value of ${∆}_{\mathrm{f}}{\mathrm{H}}^{⊝}$ is-

1. Zero

2. $<{∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$

3. $>{∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$

4. Equal to ${∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$

In an adiabatic process, no transfer of heat takes place between the system and its surroundings. The correct option for free expansion of an ideal gas under adiabatic condition from the following is:

1. $\mathrm{q}=0, ∆\mathrm{T}\ne 0, \mathrm{W}=0$

2. $\mathrm{q}\ne 0, ∆\mathrm{T}=0, \mathrm{W}=0$

3. $\mathrm{q}=0, ∆\mathrm{T}=0, \mathrm{W}=0$

4. $\mathrm{q}=0, ∆\mathrm{T}=0, \mathrm{W}\ne 0$

The pressure-volume work for an ideal gas can be calculated by using the expression $\mathrm{W}={\int }_{{\mathrm{V}}_{\mathrm{i}}}^{{\mathrm{V}}_{\mathrm{f}}}{\mathrm{p}}_{\mathrm{ex}}d\mathrm{V}$.

The work can also be calculated from the pV-plot by using the area under the curve within the specified limits.
An ideal gas is compressed (a) reversibly or (b) irreversibly from volume ${\mathrm{V}}_{\mathrm{i}}$ to ${\mathrm{V}}_{\mathrm{f}}$.
The correct option is:

1. $\mathrm{W} \left(\mathrm{reversible}\right)=\mathrm{W} \left(\mathrm{irreversible}\right)$

2. $\mathrm{W} \left(\mathrm{reversible}\right)<\mathrm{W}\hspace{0.17em}\left(\mathrm{irreversible}\right)$

3. $\mathrm{W} (\mathrm{reversible})>\mathrm{W} (\mathrm{irreversible})$

4. $\mathrm{W} \left(\mathrm{reversible}\right)=\mathrm{W} \left(\mathrm{irreversible}\right)+{\mathrm{p}}_{\mathrm{ex}}.∆\mathrm{V}$

The entropy change can be calculated by using the expression $∆\mathrm{S}=\frac{{\mathrm{q}}_{\mathrm{rev}}}{\mathrm{T}}$. When water freezes in a glass beaker, the correct statement among the following is:

Based on the reactions, ascertain the valid algebraic relationship:
$\left(i\right)$ $C\left(g\right)$ $+4H$ $\left(g\right)$ $\to C{H}_4\left(g\right);$ $$
$∆H_r$ $=x$ $kJ$ $mo{l}^{-1}$
$\left(ii\right)$ $C\left(graphite\right)$ $+$ $2H_2$ $\left(g\right)$ $\to$ $$ $C{H}_4;$ $$
$∆H_r$ $$ $=$ $y$ $kJ$ $mo{l}^{-1}$

The enthalpies of elements in their standard states are taken as zero. The enthalpy of formation of a compound is-

Consider the following statement:

"A thermodynamic quantity is a state function"

The correct option is-

1. Used to determine heat changes

2. Whose value is independent of the path

3. Used to determine pressure-volume work

4. Whose value depends on temperature only.

What is a necessary condition for an adiabatic process to occur?

1. ∆T = 0

2. ∆P = 0

3. q = 0

4. w = 0

The enthalpy of formation of all elements in their standard state is-

$∆\mathrm{U}°$ $$for combustion of methane is –x kJ mol^–1.

The value of $∆\mathrm{H}°$ for the same reaction would be:

$1.$ $=$ $∆\mathrm{U}°$
$2.$ $>$ $∆\mathrm{U}°$
$3.$ $<$ $∆\mathrm{U}°$
$4.$ $=0$