A gas fills a 100 mL cylinder fitted with a piston at a particular temperature and pressure.

Question

A gas fills a 100 mL cylinder fitted with a piston at a particular temperature and pressure. If the volume of the gas is halved by pushing in the piston, and at the same time the absolute temperature is doubled, what will happen to the pressure of the gas? (Show all calculations

Answer 1

Use the ideal gas relation

 

P₁V₁/T₁ = P₂V₂/T₂

 

Given:

 

V₂ = V₁/2

T₂ = 2T₁

 

Plug these into the relation and solve for P₂.

 

P₁V₁/T₁ = P₂(V₁/2) / (2T₁)

 

P₁ = P₂/4

 

P₂ = 4P₁

 

The final pressure is 4 times the initial pressure.  A pressure increase makes sense because you are compressing the gas and making it hotter at the same tine, which results in higher pressure.

 

Answer 2

My mistake. I misread the problem as volume being halved and temperature being halved instead of doubled.