Boyle's Law and Applied pressure

[nmsurobert]

When using a Boyle's Law Apparatus, pressure applied to the plunger can be calculated by knowing the mass of the object on the plunger and the area of the plunger. P = F/A.

The change of pressure inside the cylinder can be calculated using Boyles Law, P₁V₁ = P₂V₂

Should the value for the pressure applied to the top of the plunger be the same as P₂, the pressure of the gas in the cylinder once the plunger has been compressed? should P₂ = F/A ?

I did some math and math shows that they aren't equal. they're close, but not the same. however, i don't know if they should be equal under ideal conditions. using P = F/A, that value is slightly larger than using P₂ = (P₁V₁)/V₂

 

[Chestermiller]

Summary: P = F/A and Boyles Law relationship

When using a Boyle's Law Apparatus, pressure applied to the plunger can be calculated by knowing the mass of the object on the plunger and the area of the plunger. P = F/A.

The change of pressure inside the cylinder can be calculated using Boyles Law, P₁V₁ = P₂V₂

Should the value for the pressure applied to the top of the plunger be the same as P₂, the pressure of the gas in the cylinder once the plunger has been compressed? should P₂ = F/A ?

I did some math and math shows that they aren't equal. they're close, but not the same. however, i don't know if they should be equal under ideal conditions. using P = F/A, that value is slightly larger than using P₂ = (P₁V₁)/V₂

Neglecting the weight of the plunger, if the temperature is constant, the pressure P2 should equal the weight.

 

[nmsurobert]

Neglecting the weight of the plunger, if the temperature is constant, the pressure P2 should equal the weight.

the weight? numerically, P₂ = mg?

 

[Chestermiller]

the weight? numerically, P₂ = mg?

Plus the atmospheric pressure. In Boyle's law, one must use the absolute pressure.

 

[nmsurobert]

Plus the atmospheric pressure. In Boyle's law, one must use the absolute pressure.

I'm taking atmospheric pressure into account. once a mass has been added to the top of the plunger,
P₂ = F/A + 101325 N/m² = (P₁V₁)/V₂?

 

[Chestermiller]

I'm taking atmospheric pressure into account. once a mass has been added to the top of the plunger,
P₂ = F/A + 101325 N/m² = (P₁V₁)/V₂?

Yes, assuming the temperature is constant.

 

[nmsurobert]

Yes, assuming the temperature is constant.

awesome. thank you!