Question

An ideal gas at 78C is in a spherical flexible container having a radius of 1.00 cm. The gas is heated at constant pressure to 888C. Determine the radius of the spherical container after the gas is heated. [Volume of a sphere 5 (4y3)pr3 .]

Answer 1

Step-by-step explanation:

Given

initial temperature
`T_1=78^(\circ)C\approx 351\ K`

initial radius
`r_1=1\ cm`

final temperature
`T_2=888^(\circ)C\approx 1161\ K`

As the gas heated at constant pressure

`P_1=P_2`

using
`PV=nRT`

thus

`(V_1)/(T_1)=(V_2)/(T_2)`

`((4\pi r_1^3)/(3))/(T_1)=((4\pi r_2^3)/(3))/(T_2)`

cancel out common terms

`(r_1^3)/(T_1)=(r_2^3)/(T_2)`

`((r_1)/(r_2))^3=(T_1)/(T_2)`

`((1)/(r_2))^3=(351)/(1161)`

`(1)/(r_2)=0.6711`

`r_2=1.489\ cm`