Calculation of Work Done in Various Thermodynamic Processes

$3$ 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

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 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:

A gas absorbs 58.63 joules of heat, when the gas expands from 2 litre at STP to 2.5 litre at 1 atm.  Calculate the Change in its internal energy in joules is

(Round off the answer up to three significant figures)

$\mathrm{q}, \mathrm{w}, \mathrm{\Delta E}$ 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 $\left(v\right).$

Five moles of an ideal gas at $293 \mathrm{K}$ is expanded isothermally from an initial pressure of $2.1 \mathrm{M} \mathrm{Pa}$ to $1.3 \mathrm{M} \mathrm{Pa}$ against at constant external $4.3 \mathrm{M} \mathrm{Pa}$. The heat transferred in this process in  $\mathrm{kJ} {\mathrm{mol}}^{-1}$ is (Rounded-off of the nearest integer) [Use $\mathrm{R}=8.314 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$]

The magnitude of word done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is___________Nm.

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

$2 \mathrm{mole}$ of an ideal gas at $27°\mathrm{C}$ expands isothermally and reversibly from a volume of $4 \mathrm{litre}$ to $40 \mathrm{litre}$. The work done (in $\mathrm{Joule})$ by the gas is $(\mathrm{R}=8 \mathrm{J}/\mathrm{mol} \mathrm{K}; \ln 10=2.3)$

Identify the incorrect statement-

The process in which an ideal gas undergoes change from $\mathrm{X}$ to $\mathrm{Y}$ as shown in following diagram is:

A certain quantity of an ideal gas is expanded from $20 \mathrm{L}$ to $60 \mathrm{L}$ isothermally in three steps. The pressure of these three states are $1.5 \mathrm{atm},1.2 \mathrm{atm}$ and $1 \mathrm{atm}$ respectively. Now, the gas is brought back to the initial state by the given three steps again. Calculate the total work done on the system during this cycle in $\mathrm{J}$. (Take : $1 \mathrm{atm}-\mathrm{L}=100 \mathrm{J}$)

An ideal gas is taken around the cycle $\mathrm{ABCA}$ as

The work done in the cyclic process is:

$16 \mathrm{g}$ oxygen gas expands at $\mathrm{STP}$, to occupy double of its original volume. The work done during the process is:

For an isothermal process for an ideal gas, $\mathrm{\Delta U}$ is equal to:

For an ideal gas ${\left(\frac{\mathrm{dU}}{\mathrm{dT}}\right)}_{\mathrm{V}}$ equals to: