Question

Air at 1.02 bar, 22°C, initially occupying a cylinder volume of 0.015 m³, is compressed reversibly and adiabatically by a piston to a pressure of 6.8 bar. Calculate : 

(i) The final temperature ; 

(ii) The final volume ; 

(iii) The work done.

Answer 1

nitial pressure, p₁ = 1.02 bar 

Initial temperature, T₁ = 22 + 273 = 295 K 

Initial volume, V₁ = 0.015 m³ 

Final pressure, p₂ = 6.8 bar 

Law of compression : pvγ = C 

(i) Final temperature : 

Using the relation,Final temperature = 507.24 – 273 = 234.24°C. 

(ii) Final volume : 

Using the relation

Final volume = 0.00387 m³. 

Now, work done on the air,

where m is the mass of air and is found by the following relation,

Work done = 2.751 kJ.

(– ve sign indicates that work is done on the air).