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

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

$2$ 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

One mol of a non-ideal gas undergoes a change of state $(2.0 \mathrm{atm}, 3.0 \mathrm{L}, 95 \mathrm{K}) \to (4.0 \mathrm{atm}, 5.0 \mathrm{L}, 245 \mathrm{K})$ with a change in internal energy, $∆\mathrm{U}$$= 30.0 \mathrm{L} \mathrm{atm}$. The change in enthalpy $(∆\mathrm{H})$ of the process in $\mathrm{L} \mathrm{atm}$ is

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

On the basis of following data , calculate the heat of reaction $(\mathrm{kJ}/\mathrm{mol})$ for the given process.

${\mathrm{CH}}_4\left(\mathrm{g}\right)+2{\mathrm{O}}_2\left(\mathrm{g}\right)\mathrm{ }\to {\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

$\mathrm{BE}(\mathrm{C}–\mathrm{H})=414\mathrm{kJ}/\mathrm{mol} , \mathrm{BE}(\mathrm{O}=\mathrm{O})=498\mathrm{kJ}/\mathrm{mol},$

$\mathrm{BE}(\mathrm{C}=\mathrm{O})=741\mathrm{kJ}/\mathrm{mol} , \mathrm{BE}(\mathrm{O}–\mathrm{H})=464\mathrm{kJ}/\mathrm{mol}$

If $20\mathrm{ }\mathrm{mL}$ of $\mathrm{HCl}$ is added to $20\mathrm{ }\mathrm{mL}$ of $\mathrm{NaOH}$ solution of same strength, $5°\mathrm{C}$ increment in temperature takes place. If $200$ $\mathrm{mL}$ of same $\mathrm{HCl}$ solution is mixed with $200\mathrm{ }\mathrm{mL}$ of same $\mathrm{NaOH}$ solution, temperature increases by-

Which of the following relationship between x and y will be true when equal volumes of $1 \mathrm{M}\mathrm{ }\mathrm{H}\mathrm{C}\mathrm{l}$ and $1 \mathrm{M}\mathrm{ }{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4$ are neutralized completely by dil. NaOH solution and $\mathrm{x}$ $\text{kcal}$ and $\mathrm{\text{y kcal}}$ heat are liberated respectively?

The value of ${\mathrm{\Delta H}}_{\mathrm{O}-\mathrm{H}}$ is $109 \mathrm{kCal}/\mathrm{mol}.$ The enthalpy of  formation of $1 \mathrm{mole}$of water in gaseous state from $\mathrm{H}\left(\mathrm{g}\right)$ and $\mathrm{O}\left(\mathrm{g}\right)$ is:

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

An ideal monoatomic gas is taken round the cycle. ABCDA as shown in figure. The work done during the cycle is