A monoatomic gas is compressed to (1/8) th of its volume adiabatically. If its initial pressure is P₀ , then increase in the pressure will be

Step-by-step solution

For an adiabatic process, the relation between pressure and volume is given by PV^ = constant . For a monoatomic gas, the ratio of specific heats is = 5 3 . Given that the initial volume is V₁ = V and the final volume is V₂ = V 8 . Using the adiabatic equation, P₁ V₁^ = P₂ V₂^ P₀ V^ 5 3 = P₂ ( V 8 )^ 5 3 P₂ = P₀ (8)^ 5 3 = P₀ (2^3)^ 5 3 = P₀ (2^5) = 32 P₀ The increase in pressure is P = P₂ - P₁ P = 32 P₀ - P₀ = 31 P₀ Answer: 31 P₀