Chemistry Thermochemistry SZABMU 2024
PMDC Verified Question 2 of 81
What will be the internal energy of a system at constant volume?
A
\( \Delta E = q + P\Delta V \)
B
\( \Delta E = q + P \)
C
\( \Delta E = 0 \)
D
\( \Delta E = q_v \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( \Delta E = q_v \)
Concept:

This is a direct derivation of the first law of thermodynamics under isochoric (constant volume) conditions.

Formula:

$$ \Delta E = q + w \quad \text{(where } w = -P\Delta V) $$

Solution:

  • Because the process occurs at constant volume, \( \Delta V = 0 \).


  • No mechanical work can be done, eliminating the work term.


  • Therefore, all heat transferred (\( q_v \)) directly alters the internal energy.


  • The relationship is mathematically stated as \( \Delta E = q_v \).


Why other options are incorrect:

Option A applies when volume is NOT constant. Option B is dimensionally invalid (adding energy and pressure). Option C implies an isothermal isolated system, which is false if heat is being added.

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