(a) In an air-conditioned room at 19.0 C, a spherical balloon had the diameter o

Question

(a) In an air-conditioned room at 19.0 C, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0 cm in diameter. What was the temperature outside in degrees Celsius? Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.

(b) A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 4.50 L ? (The temperature was held constant.)

Explanation / Answer

Diameter of sphere = 50cm and radius= 25cm

Volume of sphere =

Volume of sphere at 19 deg.c, V1= (4/3)*3.142*(25)3 cm3 at 19 deg.c (19+273.15= 292.15K)

Volume of sphere at unknown temperature, V2 = (4/3)*3.142*(25.5)3

Since PV= nRT

P and n remain constant and R is anyway constant

There fore  

V1/T1= V2/T2

Where V1 and T1 are Volume and temperature before expansion and V2, T2 are volume and temperature after expansion

V2/V1= T2/T1

(25.5)3/253= T2/292.15, T2= 310.03 K

2.

from PV= nRT

P and T are constant

V1/n1= V2/n2

moels of helium before additino , n1= mass/Molecular weight = 2/ 4 =0.5, V1= 2L and V2= 4.5

2/0.5= 4.5/n2

n2= 4.5*0.5/2 =1.125 moles

Mass of helium final =1.125*4=4.5 gms

mass of helium to be added = 4.5-2 =2.5 gms

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