Question

0.5 m3 of air at pressure of 0.3 bar is compressed isothermally to 0.1
m3.Calculate final pressure, heat supplied, work done and change in intemal
energy.?? solution of this​

Answer 1

Given info : 0.5 m³ of air at pressure of 0.3 bar is compressed isothermally to 0.1 m³ .

To find : (i) final pressure (ii) heat supplied (iii) work done (iv) change in internal energy.

solution : (i) for isothermal process,

P₁V₁ = P₂V₂

⇒0.3 bar × 0.5 m³ = P₂ × 0.1 m³

⇒P₂ = 1.5 bar

Therefore the final pressure is 1.5 bar.

In isothermal process, change in internal energy equals to zero because change in temperature = 0.

so, heat supplied = work done = P₁V₁ ln[V₂/V₁]

= 0.3 bar × 0.5 m³ ln[0.1 m³/0.5m³]

= 0.15 bar m³ ln[5¯¹ ]

= -0.15 × 10⁵ ln [5] joule [ 1 bar m³ = 10⁵ J]

= -1.5 × 1.6094 × 10⁴ J

= -2.41 × 10⁴ J

therefore the heat supplied is -2.41 × 10⁴ J

And also workdone is -2.41 × 10⁴ J