A diesel engine has a compression ratio of 20: 1 . If the initial pressure is 1 10^5 ~Pa and the initial volume of the cylinder is 1 10⁻³ ~m ^3 , then how much work does the gas do during the compression? (Assume the process as adiabatic) (C_V=20.8 ~J / mol K , _ air =1.4,(20)^ 1.4 =66.3 )

Step-by-step solution

Compression ratio = Initial volume Final volume = 20 1 aligned V₁ V₂ & = 20 1 V₂ & = V₁ 20 = 10⁻³ 20 ~m ^3 aligned In adiabatic process, aligned p₁ V₁^ & =p₂ V₂^ p₂ & = ( V₁ V₂ )^ p₁ aligned Given, initial pressure, p₁=10^5 ~Pa , =1.4 p₂= ( 20 1 )^ 1.4 10^5=66.3 10^5 ~Pa Now, work done in adiabatic compression by gas, W= p₁ V₁-p₂ V₂ -1 W= 10^5 10⁻³-66.3 10^5 10⁻³ 20 1.4-1