QJEEM19Ch86b3: JEE Main 2019 Chemistry - Class 11 JEEM19Ch86b3 Solution: Which one of the following equations does not correctly…

From 1^st law of thermodynamics we know,

$$\mathrm{\Delta }$$U = q + W

Option A :

In adiabatic process exchage of heat = 0

$$\therefore$$ q = 0

$$\therefore$$ From 1st law of thermodynaics, $$\mathrm{\Delta }$$U = W

So option A is wrong.

Option B :

U is a state function. In cyclic process, initial state and final state both are same. So change in all the state function in cyclic process will be zero.

$$\therefore$$ $$\mathrm{\Delta }$$U = 0

$$\therefore$$ From 1st law of thermodynaics,

q + W = 0 $$\Rightarrow$$ q = -W

So option B is correct..

Option C :

In isochoric process volume (V) is constant. So dV = 0.

We know, W = $$-\int P_{ex}dV$$

$$\therefore$$ W = 0

$$\therefore$$ From 1st law of thermodynaics,

$$\mathrm{\Delta }$$U = q

So option C is correct.

Option D :

In isothermal process temerature (T) is constant. So dT = 0.

We know, $$\mathrm{\Delta }$$U = nC_vdT

$$\therefore$$ $$\mathrm{\Delta }$$U = 0

$$\therefore$$ From 1st law of thermodynaics,

q + W = 0 $$\Rightarrow$$ q = -W

So option D is correct.