Match the following (A) Isothermal process (i) q = ∆ U (B) Adiabatic process (ii) W = - P × &#916…

An isothermal process is the one during which the system's temperature remains constant. So change in internal energy is zero. And work can be calculated as

$\mathrm{W}=-\mathrm{nRTln}\left(\frac{{\mathrm{V}}_{\mathrm{f}}}{{\mathrm{V}}_{\mathrm{i}}}\right)$
An isobaric process is the one during which the system's pressure does not change.

So, work done will be $\mathrm{W}=-\mathrm{P}\times \mathrm{\Delta V}$
An isochoric process is the one during which the system's volume does not change. due to which work done is always zero. so, according to the first law of thermodynamics. $\mathrm{q}=∆\mathrm{U}$
An adiabatic process is the one during which no heat is transferred to or from the system, i.e., $\text{Δ}\mathrm{Q}=0$ . Hence, $\mathrm{W}=∆\mathrm{U}$

Type of processes	Feature
Isothermal	$\mathrm{W}=-\mathrm{nRTln}\left(\frac{{\mathrm{V}}_{\mathrm{f}}}{{\mathrm{V}}_{\mathrm{i}}}\right)$
Isobaric	$\mathrm{W}=-\mathrm{P}\times \mathrm{\Delta V}$
Isochoric	$\mathrm{q}=∆\mathrm{U}$
Adiabatic	$\mathrm{W}=∆\mathrm{U}$