Thermodynamic polytropic compression

[Vathral]

Homework Statement

I'm reading through my textbook and doing examples on polytropic process. I see this step and cannot figure out how the textbook gets V₃ = 0.0169 m³

P₂V₂ⁿ = P₃V₃ⁿ
(500 kPa)(0.05364 m³)^1.2 = (2000 kPa)V₃^1.2
V₃ = 0.01690 m³

Homework Equations

Not sure what to add other than it is a polytropic compression process

The Attempt at a Solution

I've tried multiplying the left side so its 26.82^1.2 then diving it it by 2000 to get rid of it from the right side to leave V₃ alone. Tried subtracting 1.2 by 1 and tried again...no dice.

 

[stewartcs]

Homework Statement

I'm reading through my textbook and doing examples on polytropic process. I see this step and cannot figure out how the textbook gets V₃ = 0.0169 m³

P₂V₂ⁿ = P₃V₃ⁿ
(500 kPa)(0.05364 m³)^1.2 = (2000 kPa)V₃^1.2
V₃ = 0.01690 m³

Homework Equations

Not sure what to add other than it is a polytropic compression process

The Attempt at a Solution

I've tried multiplying the left side so its 26.82^1.2 then diving it it by 2000 to get rid of it from the right side to leave V₃ alone. Tried subtracting 1.2 by 1 and tried again...no dice.

Solve for V3:

$$V_3 = \left(\frac{V_2^nP_2}{P_3}\right)^{1/n}$$

CS