Question

Although heat is a path function but heat absorbed by the system under certain specific conditions is independent of path. What are those conditions? Explain.

Answer 1

Heat is a path function but is changed into state function. Sometimes, when heat is absorbed by the system, it is independent of the path. There are two conditions where heat is independent of path.

i) At constant Volume

By the first law of thermodynamics, we have

$q\quad =\quad \Delta U\quad +\quad \left( -w \right)$

$q\quad =\quad \Delta U\quad +\quad p\Delta V\quad \left( Since,\quad -w\quad =\quad p\Delta V \right)$

Since volume is constant, which implies ∆V = 0,  

$\therefore \quad qv\quad =\quad \Delta U\quad +\quad 0$

$\Rightarrow \quad qv\quad =\quad \Delta U$, Which is the change in internal energy.  

ii) At Constant Pressure  

${ q }_{ p }\quad =\quad \Delta U\quad +\quad p\Delta V$

But, we have $\Delta H\quad =\quad \Delta U\quad +\quad p\Delta V$

$\therefore \quad { q }_{ p }\quad =\quad \Delta H,$ Which is the change in enthalpy.

Answer 2

Explanation:

Although heat is path function but heat absorbed by the system under certain specific conditions is independent of path. ... The two conditions under which heat becomes independent of path are (t) when volume remains constant. (it) when pressure remains constant.