1 ~mm ³ of a gas is compressed at 1 atmospheric pressure and temperature 27^ C to 627^ C . What is the final pressure under adiabatic condition? ( for the gas =15 )

Step-by-step solution

Given, V₁=1 ~mm ³ aligned &=10⁻⁹ ~m ³ p₁ &=1 ~atm &=1 10⁵ ~N / m ² T₁ &=27+273 &=300 ~K T₂ &=627+273 &=900 ~K aligned Under adiabatic condition, aligned & p₁^ 1- T₁^ =p₂^ 1- T₂^ ( p₂ p₁ )^ 1- &= ( T₁ T₂ )^ ( p₂ p₁ )^ 1-1.5 &= ( 300 900 )^ 1.5 & ( p₂ p₁ )^ -0.5 = ( 1 3 )^ 1.5 & ( p₁ p₂ )^ 0.5 = ( 1 3 )^ 1.5 aligned p₁ p₂ = ( 1 3 )^ 15 05 = ( 1 3 )³= 1 27 p₂=27 p₁=27 1 10⁵=27 10⁵ ~N / m ²