NEETPhysicsThermodynamics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If an ideal gas undergoes a thermodynamic process where its volume is directly proportional to the square of its absolute temperature ( V T^2 ), its pressure will decrease as it expands. Reason (R): In this process, the pressure of the gas is inversely proportional to the square root of its volume
Options
- ABoth Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason (R) are correct but Reason (R) is not the correct explanation of Assertion (A).
- CAssertion (A) is correct but Reason (R) is not correct.
- DAssertion (A) is not correct but Reason (R) is correct.
Correct answer
A. Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
Step-by-step solution
From the Assertion, the process follows the relation V T^2 . This can be rewritten as T V^ 1/2 . According to the ideal gas equation, PV = nRT , which implies P T V . Substituting the relation for T into the pressure proportionality: P V^ 1/2 V P V^ -1/2 P 1 V This shows that the Reason (R) is a correct statement. Because P 1 V , an increase in volume V (expansion) will lead to a decrease in pressure P . Thus, the Assertion (A) is also correct. Since the inverse relationship between pressure and the square root of