You have a gas at 25 ∘C confined to a cylinder with a movable piston.

Which of the following actions would double the gas pressure?

Check all that apply.

A. Heating the gas so that its temperature rises from 25 ∘C to 50 ∘C, while keeping the volume constant.

B. Lifting up on the piston to double the volume while keeping the temperature constant.

C. Pushing down on the piston to halve the volume while keeping the temperature constant.

D. None of the above.

Relevance

.

Temperature in this case is the absolute temperature

Pressure Law: Constant Volume

P/T = k

P₁/T₁ = P₂/T₂

Boyle’s Law: Constant Temperature

PV = k

P₁V₁ = P₂V₂

Charles’ Law: Constant Pressure

V/T = k

V₁/T₁ = V₂/T₂

( i ) constant volume

P₁/T₁ = P₂/T₂ ; Doubling absolute temperature would double the pressure

25℃ = (25 + 273 ) K = 298K

50℃ = (50 + 273 ) K = 323K

but 323K is not twice 298K so choice A is incorrect

P₂ = T₂( P₁/T₁ )

P₂ = (T₂/ T₁ ) P₁

P₂ = ( 323/298) P₁

P₂ = 1.08 P₁

( ii ) constant temperature

P₁V₁ = P₂V₂ ; Doubling the volume would halve the pressure; so choice B is incorrect

P₂ = P₁V₁ / V₂

P₂ = P₁V₁ / ( 2V₁ )

P₂ = ½P₁

( iii ) constant temperature

P₁V₁ = P₂V₂ ; Halving the volume would double the pressure; so choice C is correct

P₂ = P₁V₁ / V₂

P₂ = P₁V₁ / ( ½V₁ )

P₂ = 2P₁

C.

• A confined gas in a cylinder with a moveable piston....

To double the pressure....

1. cut the volume in half while keeping the temperature constant

2. double the absolute temperature (i.e. Kelvin) while keeping the volume constant

3. reduce the volume while watching the pressure gauge and allow temperature to increase as well.

(A) is incorrect since the temperature is not in absolute units (i.e. Kelvin)

(B) doubling the volume will cut the pressure in half

(C) that's the one