Question

A high-altitude balloon is filled with \[1.41 \times {10^4}\;L\] of hydrogen at a temperature of $21^\circ C$ and a pressure of \[745\,{\rm{ }}{Torr}\]. What is the volume of the balloon at a height of \[20km\], where the temperature is $ - 48^\circ C$ and the pressure is \[63.1\,{\rm{ }}Torr\].
A. $1.274 \times {10^5}L$
B. $1.66 \times {10^5}L$
C. \[1.66 \times {10^4}L\]
D. None of these.

Answer 1

Hint: The ratio of product of pressure and volume of the first balloon to the temperature at which first balloon lies is equal to the ratio of product of pressure and volume of the second balloon to the temperature at which the second balloon lies. Types of Pressures are Absolute, Atmospheric, Differential, and Gauge Pressure.
Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area.

Complete step by step answer:
Given:
Pressure of first balloon = \[{P_1} = 745\, {\rm{ }}{Torr}\]
Volume of first balloon = \[{V_1} = 1.41 \times {10^4}\;L\]
Temperature of the first balloon = ${T_1} = 21^\circ C$
Pressure of first balloon = \[{P_2} = 63.1\,{\rm{ }}Torr\]
Temperature of the first balloon = ${T_2} = - 48^\circ C$
Temperature of first balloon =$(273 + 21)K$ = $294\,K$
Temperature of second balloon =$(273 - 48)K$ = $225\,K$
Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area.
We know that- the ratio of product of pressure and volume of the first balloon to the temperature at which first balloon lies is equal to the ratio of product of pressure and volume of second balloon to the temperature at which the second balloon lies.
$\Rightarrow \dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
$\Rightarrow \dfrac{{745 \times 1.41 \times {{10}^4}}}{{294}} = \dfrac{{63.1 \times {V_2}}}{{225}}$
$\Rightarrow {V_2} = \dfrac{{745 \times 1.41 \times {{10}^4} \times 225}}{{294 \times 63.1}}$
$\Rightarrow {V_2} = 1.274 \times {10^5}\,L$

Hence, we can say option (A) is the correct answer.

Note:
The ratio of product of pressure and volume of the first balloon to the temperature at which the first balloon lies is equal to the ratio of product of pressure and volume of the second balloon to the temperature at which second balloon lies. Types of Pressures are Absolute, Atmospheric, Differential, and Gauge Pressure