Calculate its final volume.

Question

An ideal gas has an initial volume of 2.0 L. If its temperature increases from 2 ℃ to 4 ℃ while its pressure remaining constant.

Answer 1

This is an example of Charles Law where pressure is constant.

V1/T1 = V2/T2

Solving for V2:

V2 = V1T2/T1 where T is in Kelvin (ºC + 273)

V2 = (2.0 L)(277K)/275K

V2 = 2.01 L = 2.015 L = 2.0 L (to 2 significant figures)

 

NOTE: with such a small change in temperature, and with only 2 significant figures used in the original question (2.0 L), the answer of 2.0 L does not show the change in volume.

Answer 2

PV=nRT    

 

 

T must be in terms of Kelvin

T_c1^o = 2 + 273=  275

Tc_{2^o =}  4 + 273 = 277

 

n cancels out

R cancels out

P cancels out

 

(PV)₁=(nRT)₁

(PV)₂=(nRT)₂

 

 

(V)₁=(T)₁
(V)₂=(T)₂

 

V₂= (V₁₎(T₂)

         (T₁)  

     = (2 Liters) ( 277 K /275 K)

     = (2 L) ( 1.007) = 2.015 Liters