Applications of First Law of Thermodynamics

$3$ 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

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, ${\left(\frac{4}{11}\right)}^{2/3}=\frac{1}{2}$)

The change in internal energy equals

The magnitude of reversible work done by an ideal gas in four different processes: isothermal expansion, adiabatic expansion, constant pressure expansion, and free expansion are ${\mathrm{W}}_{\mathrm{i}}, {\mathrm{W}}_{\mathrm{a}}, {\mathrm{W}}_{\mathrm{p}}$, and ${\mathrm{W}}_{\mathrm{f}}$ respectively. Choose the right order of sequence for the magnitude of the work done. (Change in the volume is same for all the processes.)

An ideal gas undergoes isothermal expansion at constant pressure. During the process:

$\mathrm{q}, \mathrm{w}, \mathrm{\Delta E}$ 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 :

$1.0 \mathrm{mol}$ of a mono-atomic ideal gas is expanded from state $\left(1\right)$ to state $\left(2\right)$ as shown in the figure. Calculate the work done for the expansion of gas in Joules from state $\left(1\right)$ to state $\left(2\right)$ at $298 \mathrm{K}$.

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

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

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

$2$ moles of an ideal gas with ${\text{C}}_{\text{Pm}}=\frac{5}{2}\text{R}$ at $1 \mathrm{atm}, 300 \mathrm{K}$ held in cylinder fitted with piston is expanded reversibly and isothermally to three times volume (initially $=\mathrm{V}$). The cylinder placed in an insulated container and pressure returned to $1 \mathrm{atm}$ adiabatically in one step when mechanical equilibrium is reached. Read the passage and answer the questions as single choice correct.

The volume at point $\mathrm{C}$ may be

For next two question please follow the same

 $2$ moles of an ideal gas with ${\mathrm{C}}_{\mathrm{Pm}}=\frac{5}{2}\mathrm{R}$ at $1 \mathrm{atm}$, $300 \mathrm{K}$ held in cylinder fitted with piston is expanded reversibly and isothermally to three times volume (initially $=\mathrm{V}$). The cylinder placed in an insulated container and pressure returned to $1 \mathrm{atm}$ adiabatically in one step when mechanical equilibrium is reached. Read the passage and answer the questions as single choice correct.

$\Delta \text{H}$ process may be

Among the following, which expression is most accurate to calculate the work done by gas in reversible isothermal expansion?

Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from $\mathrm{x}=0\mathrm{m}$ to$\mathrm{x}=35\mathrm{m}$ by the shown force is equals to

Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from $({\mathrm{P}}_{\mathrm{i}}, {\mathrm{V}}_{\mathrm{i}})$ to $({\mathrm{P}}_{\mathrm{f}}. {\mathrm{V}}_{\mathrm{f}})$. With the help of a $\mathrm{PV}$ plot compare the work done in the above case with that carried out against a constant external pressure ${\mathrm{P}}_{\mathrm{f}}.$