CK-12-Physics - Intermediate

14.1. The Ideal Gas Law http://www.ck12.org

Illustrative Example 14.1.3

A spherical helium balloon of radius 20.00 cm is initially inflated to a pressurePiof 1.05 atm at a temperature of
30. 00 ◦C. The balloon remains in direct sunlight and the temperature of the helium increases to 37. 00 ◦C. If the
pressure inside the balloon increases by 1.00%, by what percent does the volume of the balloon increase?

Answer:

Since the number of moles remains unchanged,PTiVii=nR=constant→

PiVi

Ti =

PfVf

Tf →Vf=

Tf

Ti

Pi

PfVi, howeverPf=Pi(^1 +^0.^01 ) =^1.^01 Pi→

Substituting for 1. 01 Pifor Pf

Vf=

Tf

Ti

Pi

Pi( 1. 01 )

Vi=

( 37. 00 + 273 )

( 30. 00 + 273 )

1

1. 01

Vi= 1. 013 Vi→Vf= 1. 013 Vi→

Percent increase in volume is 1. 013 − 1. 000 = 0. 013 → 1 .3%

Illustrative Example 14.1.4

Boltzmann’s constantk, is defined ask=NRA. Show that the internal energy of a gas can be stated asU=^32 nRT.

Answer:

IfNRAis substituted forkinU=^32 kNT, thenU=^32 NNART.

ButNNA=n, sinceNis the total number of particles divided by the number of particles in one moleNA. We can

therefore state thatU=^32 nRT.

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