A gas having = 5 2 and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

Step-by-step solution

The problem describes an adiabatic compression process, governed by the relation PV^ = constant , where = 5 2 . Given initial pressure P₁ = P , initial volume V₁ = 360 c.c. , and final volume V₂ = 90 c.c. , the adiabatic relation yields P₁ V₁^ = P₂ V₂^ . Solving for final pressure, P₂ = P₁ ( V₁ V₂ )^ = P ( 360 90 )^ 5/2 . Since 360 90 = 4 , and 4^ 5/2 = (4^ 1/2 )^5 = 2^5 = 32 , it follows that P₂ = 32P . This matches option D. Final answer: D