Question

What is the minimum pressure required to compress $ 460d{m^3} $ of air at $ 2 $ bar to $ 230d{m^3} $ at $ {30^0}C $ ?

Answer 1

Hint: Air is nothing but the group of gases like oxygen, nitrogen, and carbon dioxide. When air is compressed at some temperature, then keep the terms like universal gas constant, moles, and temperature as constant. By substituting the varying pressure and volume gives the required volume.
 $ {P_1}{V_1} = {P_2}{V_2} $
 $ {P_1} $ is the pressure before compression
 $ {V_1} $ is the pressure before compression
 $ {P_2} $ is the pressure after compression
 $ {V_2} $ is the volume after compression.

Complete Step By Step Answer:
Given that air is compressed. Air is a group of gases like oxygen, nitrogen, and carbon dioxide. Ideal gas equation relates the terms like pressure, volume, temperature, number of moles, ideal gas constant.
As the volume and temperature are varied, the pressure, and volume is equal to some constant value, let the constant value be $ k $
The ideal gas equation can be written as $ PV = k $
Thus, when air is compressed, the varying terms are related as $ {P_1}{V_1} = {P_2}{V_2} $
Given pressure is $ 2 $ bar
The volume before and after compression are $ 460d{m^3} $ and $ 230d{m^3} $
Substitute the given values in the above formula,
 $ 460 \times 2 = 230 \times {P_2} $
By further simplification, the value of pressure will be $ {P_2} = 4bar $
Thus, the minimum pressure required to compress $ 460d{m^3} $ of air at $ 2 $ bar to $ 230d{m^3} $ at $ {30^0}C $ is $ 4bar $ .

Note:
Given that air is compressed at $ {30^0}C $ , it means the temperature is constant. As it is a same or group of gases, the number of moles is also constant, and the ideal gas constant is always constant. Thus, the ideal gas equation $ PV = nRT $ can be written as $ PV = k $