Question

A sample of an ideal gas at 8.50oC is trapped inside a spherical balloon having a radius of 1.8 cm. If the gas is heated at constant pressure to 93.7oC, what will be the new radius of the sphere? Recall that the volume of a sphere is given by

Answer 1

Here we can apply Charle's law,

V₁ / T₁ = V₂ / T₂

V1 = Initial volume = 24.424 cm³ ( calculated below) V2 = Final volume = ?

T1 = Initial temp = 8.50^oc + 273 = 281.5 K

T2 = Final temp = 93.7 ^oc + 273 = 366.7 K

We need to calculate the volume of ballon at 281.5 K

Volume f balloon = 4/3 x $\pi$ x r³

= 4/3 x 3.141 x (1.8 )³

= 4/3 x 3.141 x 5.832

= 73.273/ 3 = 24.424 cm³

Putting this values in Charles equation,

24.424 / 281.5 = V2 / 366.7

0.0867 = V2 / 366.7

V2 = 0.0867 x 366.7

= 31.816 cm³

Then radius is calculated by,

Volume V = 4/3 x $\pi$ x r³

31.816 = 4/3 x 3.141 x r³

   r³ = ( 31.816 x 3 ) / ( 4 x 3.141 )

= 95.448 / 12.564

r³ = 7.596

r = 1.966 cm

New radius of sphere is 1.966 cm