In an adiabatic process oxygen gas in a container is compressed along a path that can be described by the following pressure p, in atm, as a function of volume V, in liters: p = p0 V-6/5. Here p0 is a constant of units atm⋅L6/5. show answer Incorrect Answer 50% Part (a) Write an expression for the work W done on the gas when the gas is compressed from a volume Vi to a volume Vf.

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Answer:

Explanation:

In case of gas , work done

W = ∫ p dV , p is pressure and dV is small change in volume

the limit of integration is from Vi to Vf .

= ∫ p dV

=  ∫ p₀[tex]V^{-\frac{6}{5}[/tex]  dV

= p₀ [tex]V^{-\frac{6}{5} +1}[/tex] / ( [tex]\frac{-6}{5} +1[/tex] )

=  - 5p₀ [tex]V^{-\frac{1}{5}[/tex]

Taking limit from Vi  to Vf

W = - 5 p₀ ( [tex]V_f^\frac{-1}{5} - V_i^{\frac{-1}{5}[/tex]  ) ltr- atm.

An expression for the work W done on the gas when the gas is compressed from a volume Vi to a volume Vf is =- 5 p₀ ( Vf -1/5 - Vi 1/5 ) ltr- atm.

What is the Process of Oxygen Gas?

In the case of gas, When the work done is:

Then, W = ∫ p dV, p is pressure and dV is a small change in volume

After that, The limit of integration is from Vi to Vf.

= ∫ p dV

= ∫ p dV - 6/5 dV

= ∫ p₀ d -6/5+1 / (-6/5 + 1)V

= - 5p₀ Vf -1/5

Now Taking the limit from Vi to Vf

Therefore, W = - 5 p₀ ( Vf -1/5 - Vi 1/5 ) ltr- atm.

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