Given, initial load,
M1=185kg Initial pressure,
p1=76cm of Hg
Initial temperature,
T1=27°C=(273+27)K=300K Final pressure at height,
p2=45cm of Hg
Final temperature,
T2=−7°C=[273+(−7)]K=266K Volume of balloon is constant,
V1=V2=V We know that, for air,
p=ρRT Now, for initial condition, we can write
ρ1=ρ1RT1 ...(i)
Similarly, for final condition, we can write
P2=ρ2RT2 ...(ii)
Dividing Eq. (i) by Eq. (ii), we get
= Substituting the given values in above expression, we get
=() ⇒= We know that, density of balloon can be written as
ρ As, volume is constant ρ ∝ M
We can write,
== ⇒= Substituting the value of
M1 in above expression, we get
M2=185×=123.54kg Thus, the load carried by balloon will be 123.54 kg.