The use of balloons has been proposed to provide a unique vantage point for scie
ID: 107710 • Letter: T
Question
The use of balloons has been proposed to provide a unique vantage point for scientific observation of Mars. The Martian atmosphere is comprised mostly of carbon dioxide (gammaco2 = 1.28, Rco2 = 189 J/kg-K) at an ambient temperature of -55 degree C and an ambient pressure of 600 N/m^2. Gravity on Mars is g_mars = 3.72 m/s^2. a) Suppose we have a canister of compressed Helium gas (gamma_He = 1.66, R_He = 2077 J/kg-K) stored at a pressure p = 20.0 times 10^6 N/m^2 at the same ambient temperature as the surrounding atmosphere. This gas is expanded through a valve to ambient pressure in order to inflate the balloon. What is the temperature of the expanded gas inside the balloon? b) The temperature from part (a) is outside the allowable thermal limits of our design. Suppose we instead adjust (via heat transfer the temperature of the gas to 200K. With the pressure inside the balloon still at equilibrium with ambient conditions, what volume of Helium is necessary to lift a 5 kg payload?Explanation / Answer
a)Given that the pressure of helium gas=20.0×10^6N/m2
R=2077J/kg -K
Now the temperature of the expanded gas can be found using gas law.
According to gas law, pV=nRT
T=pV/nR
Converting R to L atm/mole-K=(pV/nR)*0.0821 (where R=0.0821is universal gas constant)
T=(20×10^6*1)/(1*2077)*0.0821=790K
b)Now the value of T is adjusted to 200K.
Payload=5kg
Now the volume is obtained by using the same principle of gas law.
pV=nRT
V=nRT/p
V=(1*2077*200*5)/(20×10^6*0.0821)=1.26m3 (5 is multiplied as the payload is 5kg)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.