Thermodynamics - closed systems

[MegaDeth]

Homework Statement

A cylinder fitted with a piston contains air at 1.0 Bar and 17°C. The gas is compressed according to the law PVⁿ = const., until the pressure is 4 bar when the specific volume is found to be 28% of the initial value. Heat is then added to the air at constant pressure until the volume is doubled. The same amount of heat is now removed from the air at constant volume.

Determine the value of the index n in the compression process.
Find also
(a) the overall change in internal energy/kg of air and
(b) the final pressure of the air.


R = 0.287 kJ/kgK, Cp = 1.005718kJ/kgK

Homework Equations

(p_s/p₁) = (T₂/T₁)^{(n/n - 1)}

The Attempt at a Solution

4 = (T₂/290)^{(n/n - 1)}

I'm not sure how to find n seeing as I haven't got T₂, any ideas?

 

[Mark44]

Homework Statement

A cylinder fitted with a piston contains air at 1.0 Bar and 17°C. The gas is compressed according to the law PVⁿ = const., until the pressure is 4 bar when the specific volume is found to be 28% of the initial value. Heat is then added to the air at constant pressure until the volume is doubled. The same amount of heat is now removed from the air at constant volume.

Determine the value of the index n in the compression process.
Find also
(a) the overall change in internal energy/kg of air and
(b) the final pressure of the air.


R = 0.287 kJ/kgK, Cp = 1.005718kJ/kgK

Homework Equations

(p_s/p₁) = (T₂/T₁)^{(n/n - 1)}

The Attempt at a Solution

4 = (T₂/290)^{(n/n - 1)}

I'm not sure how to find n seeing as I haven't got T₂, any ideas?

Isn't T₂ = T₁?

The same amount of heat is now removed from the air at constant volume.

BTW, your relevant equation is incorrectly written. In some places you have more parentheses than you need (e.g., (p_s/p₁) is the same as p_s/p₁ ) , and in the exponent on the right side, there are not enough of them.

Your exponent, as written, is equal to zero. n/n - 1 is the same as (n/n) - 1 = 1 - 1 = 0. If you mean $\frac{n}{n - 1}$ rather than $\frac n n - 1$, write it as (n/(n - 1)).

 

[MegaDeth]

How will that work then?

 

[Chestermiller]

You know the ratio of the specific volumes and the ratio of the pressures. This gives you enough information to get n.