A ballon at STP can lift a total mass of 175 kg attached with it.When the barometer reads 50 cmHg and the temperature becomes -10^@C at an upper point to where the balloon rises, find the maximum mass that can be lifted.Consider the volume of the balloon to be a constant.

A ballon at STP can lift a total mass of 175 kg attached with it.When

1.	A ballon at STP can lift a total mass of 175 kg attached with it.When the barometer reads 50 cmHg and the temperature becomes -10^@C at an upper point to where the balloon rises, find the maximum mass that can be lifted.Consider the volume of the balloon to be a constant.
Answer» Solution :The change in lifting CAPACITY is due to the change in the upthrust,as the density of air CHANGES at higher ALTITUDE due to the change in TEMPERATURE and pressure. Let V=volume of the balloon, `p_1`=density at STP `p_2`=density at 50 CMHG and `-10^@C` ,M=mass it can carry at the given altitude. Hence from Archimedes principle, `Vp_1=175 kg`and `Vp_2=M kg` Now, `p_1/(p_1T_1)=p_2/(p_2T_2) or,p_1/(Vp_1T_1)=p_2/(Vp_2T_2)` Subsituting the corresponding values, we get `76/(175 times 273)=50/(M times 263)` or, `M=(175 times 273 times 50)/(263 times 76)=119.5 kg`.