MHT CET · Chemistry · Thermodynamics (C)

Based on first law of thermodynamics which of the following is correct

A For an isobaric process, $q_{p} = Δ U + w$
B For an adiabatic process, $Δ U = - w$
C For an isochoric process, $Δ U = - q_{v}$
D For an isothermal Process, $q = + w$

Verified Solution

Answer & Solution

Correct Answer

(A) For an isobaric process, $q_{p} = Δ U + w$

Step-by-step Solution

Detailed explanation

In isobaric process, pressure is constant and volume increase from

V_{1}

V_{2}

due to the absorption of heat. According to the first law of thermodynamics,

Δ U = q + W

At constant pressure,

q_{p} = Δ U - W

q_{p} = Δ U - p Δ V

q_{p} = U_{2} - U_{1} - (- p (V_{2} - V_{1}))

q_{p} = (U_{2} + p V_{2}) - (U_{1} + p V_{1})

q_{p} = H_{2} - H_{1}

q_{p} = Δ H . . . (i)

As we know,

Δ H = Δ U + p Δ V

Δ H = Δ U + W

Putting the value of

Δ H

in (1)

q_{p} = Δ U + W

Other corrected options are as follows:

•

For adiabatic process,

Δ U = W

•

For an isochoric process,

Δ U = q_{v}

•

For an isothermal process

q = - W

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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