Question

Large helium–filled balloons are used to lift scientific equipment to high altitudes. What is the pressure inside such a balloon if it starts out at sea level with a temperature of 9.0°C and rises to an altitude where its volume is fifteen times the original volume and its temperature is -40.0°C.What is the gauge pressure in atm)

Answer 1

Answer:

-0.94492 atm

Explanation:

$P_1$ = Initial pressure = 1 atm

$V_1$ = Initial volume

$T_1$ = Inital temperature = 9°C

$P_2$ = Final pressure

$V_2$ = Final volume = $15V_1$

$T_1$ = Final temperature = -40°C

We have the relation

$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\\\Rightarrow P_2=\dfrac{P_1V_1T_2}{T_1V_2}\\\Rightarrow P_2=\dfrac{1\times V_1\times (273.15-40)}{(273.15+9)\times 15V_1}\\\Rightarrow P_2=0.05508\ atm$

Gauge pressure is given by

$P_g=P_2-P_a\\\Rightarrow P_g=0.05508-1\\\Rightarrow P_g=-0.94492\ atm$

The gauge pressure is -0.94492 atm