Question

How many times is the weight of air filling a room in winter ( \[{7^ \circ }C\] ) greater than weight in summer ( ${37^ \circ }C$ ) ? Assume that pressure is constant.
A. $1.11$
B. $0.90$
C. $11.1$
D. $9.0$

Answer 1

Hint: The general gas equation is also called ideal gas law and to solve this question one must have a concept of this topic and in this question, we will use another version of general gas law that is the density version and using that we will solve this question and we will get our required solution.

Formula used:
$PV = nRT$
Where, $P$ is the pressure, $V$ is the volume, $n$ is the amount of substance, $R$ is the ideal gas constant and $T$ is the temperature.

Complete step by step answer:
As we know that,
$P{M_0} = dRT$
This is nothing but the density version of the ideal gas law.In which, $d$ is the density and ${M_0}$ is the molar mass.From this equation $P{M_0} = dRT$ we can say that,
$d \propto \dfrac{1}{T}$
And we can say that,
\[{\text{Weight of the gas}} \propto \dfrac{1}{T}\]
So, we can write as,
$\therefore \dfrac{{{{\text{W}}_{winter}}}}{{{{\text{W}}_{summer}}}} = \dfrac{{273 + 37}}{{273 + 37}} = 1.11$

Hence, the weight of air filling a room in winter is $1.11$ greater than weight in summer.

Note: The air we breathe has a specific density, and it presses on everything it comes into contact with. Atmospheric pressure, often known as air pressure or barometric pressure, is the measurement of pressure in the atmosphere. The force produced on a surface by the air above it as gravity drags it to the ground is known as air pressure. Fair skies, as in clear weather, are frequently connected with high air pressure. When the air cools, the density of the air increases, causing the air to be pushed down. Because the air is pushed down, the pressure of the air rises as more space is created for more air to fill.