Dodgy solution for a thermodynamics problem?

[aspodkfpo]

Homework Statement

n/a

Relevant Equations

PV=nrT

https://www.asi.edu.au/wp-content/uploads/2020/07/ASOE_Physics_2019-answers.pdf

Question 14 B) Re: " The graph of force per area vs amount of gas will change, as the pressure is increasing due to increasing temperature, so the amount of gas in a volume at a given pressure will be decreasing. This will have the effect of decreasing the maximum force per area for there to be no gas in the bubble, and also decreasing the rate of increase of force per area beyond that point. "

Cannot understand this, can someone explain this more? Also with their reasoning it seems that they ignore that the pressure rise in the first scenario also causes an increasing temperature?

 

[kuruman]

I think what it is trying to say without equations is this.
First, the ideal gas law in 14(b) is written as $pV=AT$ where $A$ is a measure of the amount of gas.
Now for a (nearly) constant volume process, $d(pV)\approx Vdp$.
The other side of the equation is $d[AT]=T dA+AdT$.
So $dp \sim T dA+AdT.$

In 14(a) there is no change in temperature so $dp \sim T dA.$
In 14(b) there is change in temperature so $dp \sim T dA +AdT.$
For the same $dA$ there is less $dp$ in 14(b) than in 14(a) point by point.