A balloon carries a total load of 185 kg at normal pressure and temperature of 27$^\circ$C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $-$7$^\circ$C. Assuming the volume constant?
Solution
P<sub>m</sub> = $\rho$RT<br><br>$\therefore$ ${{{P_1}} \over {{P_2}}} = {{{\rho _1}{T_1}} \over {{\rho _1}{T_2}}}$<br><br>$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{P_1}{T_2}} \over {{P_2}{T_1}}} = \left( {{{76} \over {45}}} \right) \times {{266} \over {300}}$$<br><br>$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{M_1}} \over {{M_2}}} = {{76 \times 266} \over {45 \times 300}}$$<br><br>$\therefore$ ${M_2} \Rightarrow {{45 \times 300 \times 185} \over {76 \times 266}} = 123.54$ kg
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
This question is part of PrepWiser's free JEE Main question bank. 271 more solved questions on Thermodynamics are available — start with the harder ones if your accuracy is >70%.