If $5 \ L$ of an ideal gas at a constant external pressure of $2 \ atm$ expands isothermally to a final volume of '$X$' $L$,the system does a work of $-2,026.4 \ J$. '$X$' (in $L$) is $(1 \ L \cdot atm = 101.32 \ J)$

The enthalpies of the elements in their standard states are assumed to be

Fill in the blanks given below:
$(i)$ $A$ system in which the exchange of energy between the system and the surroundings is possible but the exchange of matter is not possible is called a .......
$(ii)$ The total amount of energy, which is the sum of the internal energy of the substance and the product of its pressure and volume, is called .......
$(iii)$ The change in energy that occurs when a chemical reaction is carried out at constant pressure is called .......
$(iv)$ The process of attaining thermal equilibrium between any two heat-conducting substances is known as the ....... law of thermodynamics.

Explain mechanical work.

When the temperature of $2$ moles of an ideal gas is increased by $20^{\circ} C$ at constant pressure,find the work involved in the process. (in $R$)

In thermodynamics,the $P-V$ work done is given by $w = -\int P_{ext} dV$. For a system undergoing a particular process,the work done is $w = -\int \left(\frac{RT}{V - b} - \frac{a}{V^2}\right) dV$. This equation is applicable to a: