VT는 일정. 1.00 cm ball 7℃ gas 88℃ (4/3)πr3

VT는 일정. 1.00 cm ball 7℃ gas 88℃ (4/3)πr3

 

 

An ideal gas at 7°C is in a spherical flexible container

having a radius of 1.00 cm.

The gas is heated at constant pressure to 88°C.

Determine the radius of the spherical container after the gas is heated.

[Volume of a sphere = (4/3)πr3]

 

---------------------------------------------------

 

V1 = (4/3)πr^3

= (4/3) (3.14159) (1.00 cm)^3

= 4.1888 cm^3

 

 

 

V1 / T1 = V2 / T2

( 참고 https://ywpop.tistory.com/1978 )

 

V2 = V1 T2 / T1

= (4.1888) (273 + 88) / (273 + 7)

= 5.40 cm^3

 

 

 

r = [ 5.40 / [(4/3) (3.14159)] ]^(1/3)

= 1.088 cm

 

 

 

 

또는

V1 / T1 = V2 / T2 에서,

(4/3)π를 소거하면,

1 / (273 + 7) = r^3 / (273 + 88)

 

r^3 = [1 / (273 + 7)] (273 + 88) = 1.2893

 

r = (1.2893)^(1/3) = 1.088 cm