Answer the following by appropriately matching the lists based on the information given in the paragraph.
In a thermodynamics process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $\mathrm{T}\mathrm{\Delta }\mathrm{X},$ where $\mathrm{T}$ is temperature of the system and $\mathrm{\Delta }\mathrm{X}$ is the infinitesimal change in a thermodynamic quantity $\mathrm{X}$ of the system. For a mole of monatomic ideal gas $\mathrm{X}=\frac{3}{2}\mathrm{R}\mathrm{l}\mathrm{n}\left(\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{A}}}\right)+\mathrm{R}\mathrm{l}\mathrm{n}\left(\frac{\mathrm{V}}{{\mathrm{V}}_{\mathrm{A}}}\right).$ Here, $\mathrm{R}$ is gas constant, $\mathrm{V}$ is volume of gas, ${\mathrm{T}}_{\mathrm{A}}$ and ${\mathrm{V}}_{\mathrm{A}}$ are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
 

	Column - I		Column - II
(a)	Work done by the system in process $1\to 2\to 3$	(p)	$\frac{1}{3}\mathrm{R}{\mathrm{T}}_0\mathrm{l}\mathrm{n}2$
(b)	Change in internal energy in process $1\to 2\to 3$	(q)	$\frac{1}{3}\mathrm{R}{\mathrm{T}}_0$
(c)	Heat absorbed by the system in process $1\to 2\to 3$	(r)	$\mathrm{R}{\mathrm{T}}_0$
(d)	Heat absorbed by the system in process $1\to 2$	(s)	$\frac{4}{3}\mathrm{R}{\mathrm{T}}_0$
		(t)	$\frac{1}{3}\mathrm{R}{\mathrm{T}}_0\left(3+\mathrm{l}\mathrm{n}2\right)$
		(u)	$\frac{5}{6}\mathrm{R}{\mathrm{T}}_0$

If the process on one mole of monatomic ideal gas is as shown in the $\mathrm{P}\mathrm{V}$ -diagram with ${\mathrm{P}}_0{\mathrm{V}}_0=\frac{1}{3}\mathrm{R}{\mathrm{T}}_0,$ the correct match is

• A

  $\mathrm{a}-\mathrm{s},\mathrm{ }\mathrm{b}-\mathrm{r},\mathrm{ }\mathrm{c}-\mathrm{q},\mathrm{ }\mathrm{d}-\mathrm{t}$
• B

  $\mathrm{a}-\mathrm{q},\mathrm{ }\mathrm{b}-\mathrm{r},\mathrm{ }\mathrm{c}-\mathrm{p},\mathrm{ }\mathrm{d}-\mathrm{u}$
• C

  $\mathrm{a}-\mathrm{q},\mathrm{ }\mathrm{b}-\mathrm{s},\mathrm{ }\mathrm{c}-\mathrm{r},\mathrm{ }\mathrm{d}-\mathrm{u}$
• Correct answer
  D

  $\mathrm{a}-\mathrm{q},\mathrm{ }\mathrm{b}-\mathrm{r},\mathrm{ }\mathrm{c}-\mathrm{s},\mathrm{ }\mathrm{d}-\mathrm{u}$

Hence, the correct answer is option: 'D'.