Question

Take temperatures and efficiencies to be exact.
A monatomic ideal gas (? = 1.67) is compressed adiabatically from a pressure of 3.00

Answer 1

Given:

Initial presure of the ideal gas , Pi = 3.00 x10⁵ Pa

when the gas under goes an adiabatic compression ,

final presure or new presure of the gas ,Pf = ?

Initial volume of the gas , Vi = 180 L or 180 x10^-3 m³

final volume of the gas , Vf = 50 L or 50 x10^-3m³

ratio of specific heats for mon-atomic gas,? = 1.67

(a)

when the gas undergoes aa adibatic compression , the

relation between presure and volume as ,

PV^? = constant

or

PiVi^? =PfVf^?

final or new presure of the gas ,

Pf = PiVi^? / Vf^?

    = Pi (Vi/Vf)^?

    ^{= (3.00 x105 )(180 /50)1.67}

    =2547689 Pa or 25.48 x10⁵ Pa

(b)

Work done during an adiabatic- compression is givenby the formula

            W= ( PiVi-  Pf.Vf ) / (?-1)

                = (3.00x10⁵ Pax 180 x10^-3 m³) - (25.48x10⁵Pa)(50 x10^-3m³)/(1.67-1)

                = (54000-127400) / 0.67

= - 10.955 x10⁴ J