Physics Thermodynamics MDCAT 2018
PMDC Verified Question 50 of 54
If one mole of an ideal gas is heated at constant pressure, then the first law of thermodynamics can be written as:
A
\(C_v \Delta T = C_p \Delta T + P \Delta T\)
B
\(C_p \Delta T = C_v \Delta T + V \Delta P\)
C
\(C_p \Delta T = C_v \Delta T + P \Delta V\)
D
\(\Delta C_v T = \Delta C_p T + P \Delta V\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \(C_p \Delta T = C_v \Delta T + P \Delta V\)
1. Concept:

The First Law of Thermodynamics states that heat supplied to a system equals the increase in internal energy plus the work done by the system.

2. Formula:

$$Q = \Delta U + W$$

3. Solution:

  • At constant pressure, heat supplied for one mole is \(Q = C_p \Delta T\).


  • The change in internal energy for any process is \(\Delta U = C_v \Delta T\).


  • The work done at constant pressure is \(W = P \Delta V\).


  • Substituting these yields: \(C_p \Delta T = C_v \Delta T + P \Delta V\).


4. Why other options are incorrect:

Other options misrepresent the basic thermodynamic terms, swapping specific heats or introducing non-standard terms like \(V \Delta P\) which applies to steady-flow processes rather than constant pressure expansion.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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