એક આદર્શ વાયુ માટે શરૂઆતી દબાણ અને કદ \(P_0\) અને \(V_0\) છે.જ્યારે વાયુને અચાનક \(\frac{ V _{ o }}{4}\) કદમાં દબાવવામાં આવે ત્યારે વાયુનું અંતિમ દબાણ ....... હશે. (\(\gamma\) = અચળ દબાણ અને અચળ કદે વિશિષ્ટ ઉષ્માનો ગુણોત્તર આપેલ છે.)

A \(P _0(4)^{\frac{1}{\gamma}}\)
B \(P _0(4)^\gamma\)
C \(P _0\)
D \(4 P _0\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(P _0(4)^\gamma\)

Step-by-step Solution

Detailed explanation

As gas is suddenly compressed, the processes is adiabatic. Equation of gas for adiabatic process is \(PV ^\gamma=\text { constant. }\) \(\Rightarrow P _1 V _1^\gamma= P _2 V _2^\gamma\) \(\Rightarrow P _0 V _0^\gamma= P _2\left(\frac{ V _0}{4}\right)^\gamma\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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