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Question: For an adiabatic compression the quality \(P{V^\gamma }\). (A) Increases (B) Decreases (C) Rem...

For an adiabatic compression the quality PVγP{V^\gamma }.
(A) Increases
(B) Decreases
(C) Remains constant
(D) Depends on γ\gamma

Explanation

Solution

Hint The compression in which there is no heat added or subtracted from the air and the internal energy of the air is increased by an amount which is equivalent to the external work on the air. Based on this concept, we can solve this question.

Complete step-by-step answer:
We know that equation of state is given by:
TVY−1=T{V^{Y - 1}} =constant
T1V1Y−1=T2V2Y−1{T_1}{V_1}^{Y - 1} = {T_2}{V_2}^{Y - 1}
T2T1=(V1V2)Y−1\dfrac{{{T_2}}}{{{T_1}}} = {\left( {\dfrac{{{V_1}}}{{{V_2}}}} \right)^{Y - 1}}
When the gas gets compressed, the temperature thus increases.
PV=nRT  PV = nRT\;
P2V2−P1V1=nR(T2−T1){P_2}{V_2} - {P_1}{V_1} = nR({T_2} - {T_1})
Since temperature increases, PV also increases.

Hence, the correct answer is Option A.

Note It should be known that the adiabatic compression of the gas causes a rise in the temperature of the gas. In the case of adiabatic expansion against pressure, or a spring, will result in the drop of the temperature. In this contrast, the free expansion is defined as an isothermal process for an ideal gas.