Question

A hot air balloon is filled with 1.37 × 106 l of an ideal gas on a cool morning (11 °c. the air is heated to 117 °c. what is the volume of the air in the balloon after it is heated? assume that none of the gas escapes from the balloon.

Answer 1

So according to Charles's law the volume of a gas is directly proportional to the absorbed absolute temperature assuming constant pressure and a closed system. Or V/T=constant. 
(V1/T1)=(V2/T2). Absolute temperature is in degrees Kelvin so:
 
T1=273.15+11= 284.15 K and T2=273.15 + 117=390.15 K. V1= 1.37*10^6 L.

We need to find V2. V2= (V1/T1)*T2.

Now we plug in the numbers: V2=(1.37*10^6/284.15)*390.15=1881068.1 L.
The volume of the air balloon when we heat the gas inside is
V2=1.88*10^6 L. 

Answer 2

We first assume the gas is an ideal gas so we can use the equation PV = nRT. At constant pressure, nR/P are constants so at any condition the ratio of V/T is the same. With this, we calculate as follows:

V1/T1 = k = V2/T2
1.37 × 10^6 L / (11+273.15) = V2 / (117+273.15)
V2 = 1881068.1 L