NEET Physics Question - Thermal Physics

Assertion (A): In adiabatic expansion of monoatomic ideal gas, if volume increases by 12%, then pressure decreases by 20%.

Reason (R): In adiabatic process \(PV^{5/3} = \text{constant}\).

(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(3) (A) is true but (R) is false

(4) Both (A) and (R) are false

Solution:

For a monoatomic ideal gas, \(\gamma = 5/3\), so \(PV^{5/3} = \text{constant}\). (R) is true. If volume increases by 12%, \(V_2 = V_1(1+0.12)\). Using \(P_1V_1^{\gamma} = P_2V_2^{\gamma}\), we get \(P_2 = P_1(1+0.12)^{-5/3}\). Using approximation \((1+x)^n approx 1+nx\) for small \(x\), \(P_2 \approx P_1(1 - (5/3)(0.12)) = P_1(1-0.20) = 0.8P_1\). Thus, pressure decreases by 20%. (A) is true. (R) correctly explains (A).

Rankers Physics

Adiabatic Expansion of Monoatomic Gas

Solution:

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