Applications of First Law of Thermodynamics

In a container $3.2 \mathrm{g}$ of oxygen gas is kept at $20 \mathrm{atm}$ and $300\mathrm{K}$. The gas is allowed to expand isothermally against constant external pressure of $1 \mathrm{atm}$ till the final pressure reaches to $1 \mathrm{atm}$. Calculate the magnitude of work done by the gas.(The nearest integer)

$0.1$ moles of a diatomic gas at $27°\mathrm{C}$ is heated at constant pressure, so that the volume is doubled. If $\mathrm{R}=2 \mathrm{cal}/\mathrm{mol}$, the work done by gas in $\mathrm{cal}$ will be

$3$ moles of an ideal gas expands isothermally against a constant pressure of $2$ Pascal from $20 \mathrm{L}\text{ to} 60$ L.The amount of work involved is

$5 \mathrm{moles}$ of an ideal monoatomic gas undergoes adiabatic expansion from $5 \mathrm{L} \text{to} 20 \mathrm{L}$ against a constant external pressure of $2 \mathrm{bar}$.

One mole of an ideal gas is taken from $\mathrm{a}$ and $\mathrm{b}$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is ${\mathrm{w}}_{\mathrm{s}}$ and that along the dotted line path is ${\mathrm{w}}_{\mathrm{d}},$ then the integer closest to the ratio ${\mathrm{w}}_{\mathrm{d}}/{\mathrm{w}}_{\mathrm{s}}$ is:

Two moles of $\mathrm{He}$ gas $(\gamma =5/3)$ are initially at temp $27°\mathrm{C}$ and occupy a volume of $20$ litres. The gas is first expanded at constant pressure until its volume is doubled. Then it undergoes reversible adiabatic change, until the volume become $110 \mathrm{lit}$, then predict the value of $\mathrm{T}/100$ (where $\mathrm{T}$ is the final temperature, ${\left(\frac{4}{11}\right)}^{2/3}=\frac{1}{2}$)

Select the incorrect statement about the above diagram.

An ideal gas undergoes adiabatic expansion against constant external pressure. Which of the following is incorrect:

Calculate $\mathrm{\Delta G}\left(\mathrm{in} \mathrm{kJ}\right)$ (in magnitude) for the process, one mole of an ideal gas at $22.4 \mathrm{litres}$ is expanded isothermally and reversibly at $300 \mathrm{K}$ to a volume of $224 \mathrm{litres}$.

Give your answer as the nearest integer.

In the given graph, the area of circle $\mathrm{A}$ and $\mathrm{B}$ are $40$ unit and $36$ unit respectively, total work done ' $\mathrm{x}$ ' unit.

When a system is taken from state$\mathrm{A}$ to $\mathrm{B}$ along path $\mathrm{A} \mathrm{C} \mathrm{B}$, as shown in the figure, $3$ unit of heat flows into the system and the system does $3$ unit of work. If ' $\mathrm{y}$ ' unit heat flows into the system along the path $\mathrm{ADB}$, and the work done by the system is $2$ unit?
Then the value of $\mathrm{x}+\mathrm{y}$ is

The enthalpy change of a reaction is independent of

$\mathrm{q}, \mathrm{w}, \mathrm{\Delta E}$ and $\mathrm{\Delta H}$ for the following process $\mathrm{ABCD}$ for a monoatomic gas are:

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $T_1$ and $T_2\left( T_1<T_2\right).$ The correct graphical depiction of the dependence of work done $\left(w\right)$ on the final volume $\left(v\right).$

A thermodynamic cycle in the pressure $\left(\mathrm{P}\right)$-volume $\left(\mathrm{V}\right)$ plane is given below:

$\mathrm{AB}$ and $\mathrm{CD}$ are isothermal processes while $\mathrm{BC}$ and $\mathrm{DA}$ are adiabatic processes. The same cycle in the temperature $\left(\mathrm{T}\right)$- entropy $\left(\mathrm{S}\right)$ plane is :

During the free expansion of an ideal gas in an isolated chamber,
 

A piston filled with $0.04 \mathrm{mol}$ of an ideal gas expands reversibly from $50.0 \mathrm{ml}$ to $375 \mathrm{ml}$ at a constant temperature of $37.0°\mathrm{C}$. As it does so, it absorbs $208 \mathrm{J}$ of heat. The values of $\mathrm{q}$ and $\mathrm{w}$ for the process will be

($\mathrm{R}=8.314 \mathrm{J}/\mathrm{mol} \mathrm{K}$) ($\ln 7.5=2.01$)

One mole of an ideal gas (at $25°\mathrm{C}$ ) is expanded from volume $1 \mathrm{L}$ to $4 \mathrm{L}$ at constant temperature. The value of work done (in $\mathrm{J}$), if gas is expanded against vacuum $\left({\mathrm{P}}_{\mathrm{ext}}=0\right)$?

For next two question please follow the same

Work done by the system in isothermal reversible process is: ${\mathrm{w}}_{\mathrm{r}\mathrm{e}\mathrm{v}}=\mathrm{ }-2.303\mathrm{ }\mathrm{n}\mathrm{R}\mathrm{T}\log \frac{{\mathrm{V}}_2}{{\mathrm{V}}_1}$ . Also in case of adiabatic reversible process work done by the system is given by: ${\mathrm{w}}_{\mathrm{r}\mathrm{e}\mathrm{v}}=\frac{\mathrm{n}\mathrm{R}}{\mathrm{\gamma }-1}[{\mathrm{T}}_2-{\mathrm{T}}_1]$ . During expansion disorder increases and the increase in disorder is expressed in terms of change in entropy $\mathrm{\Delta }\mathrm{S}=\frac{\mathrm{\Delta }\mathrm{H}}{\mathrm{T}}$ . Both entropy and enthalpy changes obtained for a process were taken as a measure of spontaneity of process but finally it was recommended that decrease in free energy is responsible for spontaneity and $\mathrm{\Delta }\mathrm{H}-\mathrm{T}\mathrm{\Delta }\mathrm{S}$.

Which of the following statements are correct:

For next two question please follow the same

A sample of an ideal gas is expanded to twice its original volume of 1 m³ in a reversible process for which $\text{α}={\text{5 atm m}}^{-6}$  and ${\text{C}}_{\text{Vm}}={\text{20 J K}}^{-1}{m}^{-1}$ at constant volume.

The work done during the process may be