Thermodynamics problem-using PV=nrt

[pyroknife]

I have attached the problem statement (untitled) and the solutions (untitled 1).

I only have a problem with the second part of the solutions starting at the line "the amount of air that needs to be bled off to restore pressure..."

The problem asks what the amount of air that must be bled off to restore pressure to its original value at this temperature is.

Doesn't that mean the temperature is constant in the equation and the pressure is changing, not the other way around like they have it in the 2 equations at the bottom that solves for mass??

My professor said the solutions was right, but I don't see how. Am I misinterpreting something?

 

[rock.freak667]

Firstly they solved for the mass at the initial temperatre to get m₁.

Then they found the mass at the final temperature m₂

the mass needed to get bled off was m₂-m₁.


Alternatively, the pressure change that was required was 26 kPa within 0.25 m³ at 50°C. So you could have used the mass from that.