The work done when $2$ moles of an ideal gas expands reversibly and isothermally from a volume of $1 \mathrm{L}$ to $10 \mathrm{L}$ at $300 \mathrm{K}$ is $\left(\mathrm{R}=0.0083 \mathrm{kJ} \mathrm{K} {\mathrm{mol}}^{-1}\right)$

[ Use $R=8.314 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$]

How much heat will be absorbed by $1$ mole of an ideal gas, if it is expanded reversibly from $5 \mathrm{L}$ to $25 \mathrm{L}$ at ${27}^o\mathrm{C}$? 

$(\log 3=0.5, \log 4=0.6, \log 5=0.7)$

One mole of an ideal gas at $27 °\mathrm{C}$ is taken from $A$ to $B$ as shown in the given $PV$ indicator diagram. The work done by the system will be _______ $\times {10}^{-1} \mathrm{J}.$ [Given, $R=8.3 \mathrm{J} {\mathrm{mole}}^{-1} \mathrm{K}, \ln 2=0.6931$] (Round off to the nearest integer)

(Round off to the nearest integer)

At $25°\mathrm{C},50 \mathrm{g}$ of iron reacts with $\mathrm{HCl}$ to form ${\mathrm{FeCl}}_2$. The evolved hydrogen gas expands against a constant pressure of $1 \mathrm{bar}$. The work done by the gas during this expansion is -_______ $\mathrm{J}$.

(Round off to the Nearest Integer)

[Given : $\mathrm{R}=8.314 \mathrm{J}{ \mathrm{mol}}^{-1}{ \mathrm{K}}^{-1}$. Assume, hydrogen is an ideal gas]

[Atomic mass off Fe is $55.85 \mathrm{u}$]

The magnitude of work done by a gas that undergoes a reversible expansion along the path $\mathrm{A}\mathrm{B}\mathrm{C}$ shown in the figure is _________.

Under the isothermal condition, a gas at $300\mathrm{ }\mathrm{K}$ expands from $0.1\mathrm{ }\mathrm{L}$ to $0.25\mathrm{ }\mathrm{L}$ against a constant external pressure of $2$ bar. The work done by the gas is

(Given that $1\mathrm{ }\mathrm{L}$ bar$=100\mathrm{ }\mathrm{J}$)

($\mathrm{U}$ : internal energy, $\mathrm{S}:$ entropy, $\mathrm{p}:$ pressure, $\mathrm{V}:$ volume, $\mathrm{R}$ : gas constant) 

(Given: molar heat capacity at constant volume, ${\mathrm{C}}_{\mathrm{V},\mathrm{m}}$ of the gas is $\frac{5}{2}\mathrm{R}$)

Give your answer as the nearest integer.

Two identical samples of gas are allowed to expand $\left(\mathrm{i}\right)$ isothermally and $\left(\mathrm{ii}\right)$ adiabatically. The amount of work done id then

The three processes in a thermodynamic cycle shown in the figure are : Process $1\to 2$ is isothermal; Process $2\to 3$ is isochoric (volume remains constant); Process $1\to 3$ is adiabatic.

The total work done by the ideal gas in this cycle is,$10 \mathrm{J}.$ The internal energy decreases by, $20 \mathrm{J}$ in the isochoric process. The work done by the gas in the adiabatic process is, $-20 \mathrm{J}$. The heat added to the system in the isothermal process is