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

Answer:

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

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

$\frac{\frac{4\pi r_1^3}{3}}{T_1}=\frac{\frac{4\pi r_2^3}{3}}{T_2}$

cancel out common terms

$\frac{r_1^3}{T_1}=\frac{r_2^3}{T_2}$

$(\frac{r_1}{r_2})^3=\frac{T_1}{T_2}$

$(\frac{1}{r_2})^3=\frac{351}{1161}$

$\frac{1}{r_2}=0.6711$

$r_2=1.489\ cm$