a weather balloon carries instruments that measure temperature,pressure and humidity as it rises through the atmosphere.Suppose such a balloon has a volume of 1.2 m^3 at sea level where the pressure is 1 atm and the temperature is 20 degree Celsius.When the balloon is at an altitude of 11 km(36,000ft) the pressure is down to 0.5 atm and the temperature is about -55 degree Celsius,what is the volume of the balloon then.
To find the volume of the balloon at an altitude of 11 km, we can use Boyle's Law and Charles's Law, which state that the pressure and volume of a gas are inversely proportional, and the volume and temperature of a gas are directly proportional, respectively.
We are given:
Initial conditions at sea level:
Volume (V1) = 1.2 m^3
Pressure (P1) = 1 atm
Temperature (T1) = 20°C = 293.15 K
Conditions at an altitude of 11 km:
Pressure (P2) = 0.5 atm
Temperature (T2) = -55°C = 218.15 K
Using Boyle's Law, we can write:
(P1 * V1) = (P2 * V2)
Rearranging the equation, we have:
V2 = (P1 * V1) / P2
Plugging in the given values, we get:
V2 = (1 atm * 1.2 m^3) / 0.5 atm
V2 = 2.4 m^3
Therefore, at an altitude of 11 km, the volume of the balloon is 2.4 m^3.