Question:
The density of air at N.T.P. is 1.293 gm/lit. If the pressure is tripled keeping its temperature constant its density becomes
The density of air at N.T.P. is 1.293 gm/lit. If the pressure is tripled keeping its temperature constant its density becomes
Updated On: Jul 7, 2022
- 3.87 gm/Itr
- 1.293 gm/Itr
- 2.586 gm/Itr
- 0.431 gm/Itr
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The Correct Option is A
Solution and Explanation
First we derive an expression for density of a gas.
Density $=\frac{\operatorname{mass}( w )}{\operatorname{volume}( V )}$
but we know that PV = nRT
now $n =\frac{ w }{ M }$ where $M$ is molecular weight
So, $PV =\frac{ w }{ M } RT$
this gives $\frac{ w }{ V }=\frac{ PM }{ RT }=$ density $= d$
Clearly at a constant temperature,
$
\frac{ d _{1}}{ P _{1}}=\frac{ d _{2}}{ P _{2}}
$
so since pressure is tripled, density also triples new density $=$ old density $x_{3}$
$=1.293 \times 3$
$=3.87 gm / ltr$
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.