Question

A very flexible helium-filled balloon is released from the ground into the air at 20. "C. The initial volume of

the balloon is 5.00 L, and the pressure is 760. ininHg. The balloon ascends to an altitude of 20 km,
where the pressure is 76.0 mmHg and the temperature is -50. "C. What is the new volume, V2, of the
balloon in liters, assuming it doesn't break or leak?​

Answer 1

V2 = 38.055 Liters

Step-by-step explanation:

• According to the combined gas law, the volume of a fixed amount of a gas is directly proportional to absolute temperature and inversely proportional to pressure.

• That is,
  `V\alpha (T)/(P)`

`V=k(T)/(P)`

• At two varying conditions of pressure, volume and pressure,

`k=(P1V1)/(T1)=(P2V2)/(T2)`

In this case;

Initial volume, V1 = 5.00 L

Initial temperature, T1 = 20°C or 293 K

Initial pressure, P1 = 760 mmHg

Final temperature, T2 = -50°C or 223 K

Final pressure, P2 = 76 mmHg

Therefore,

we can determine the known variables in the formula to determine the unknown variable, V2.

`V2 = (P1V1T2)/(T1P2)`

`V2=((5)(760)(223))/((293)(76))`

`V2=38.055l`

Thus, the new volume is 38.055 Liters