Question

How do you convert a pressure of $ 1.75 $ atm to kPa and to mmHg?

Answer 1

Hint :Pressure is defined as the force acting per unit area. SI Unit of pressure is Pascal (Pa). atm, kPa mmHg are other units which are used to measure pressure. All these units are interconvertible into each other if we know the common mathematical formula/equation connecting them.

Complete Step By Step Answer:
Pascal, the SI unit of pressure can be defined as one Newton of force acting over one square meter of area. But we should remember that in daily life pressure is mostly measured in other units such as atm, kPa, mmHg.
Atm is defined as the unit of pressure which is equal to the air pressure at sea level.
Now, we know that $ 1 $ atm = $ 1.01325 $ bar
We should also remember that $ 1\,bar=\,{{10}^{5}} $ Pascal
Therefore, from above two expressions we can conclude that $ 1 $ atm = $ 1.03125\times {{10}^{5}} $ Pascal
Also, we know that $ 1 $ pascal (Pa)= $ {{10}^{-3}} $ kPa
Therefore, we get that $ 1\,atm=\,1.01325\times {{10}^{2}}kpa $
In question we are asked to convert $ 1.75atm $ to kPa
 $ \therefore $ $ 1.75atm=1.75\times 1.01325\times {{10}^{2}}=177\,kPa $
Hence, we can say that there are $ 177 $ kPa in $ 1.75 $ atm
Now, let’s solve the other part of the question, that is to convert $ 1.75 $ atm to mmHg
We know that $ 1\,atm=760mmHg $
So, to convert $ 1.75 $ atm to mmHg we will simply multiply the given value of atm with $ 760 $
Therefore, $ 1.75atm=1.75\times 760=1330 $ mmHg
Hence, we see that there is $ 1330 $ mmHg in $ 1.75 $ atm of pressure.

Note :
One should always learn the formula interconnecting different units to solve the problem easily. It should be noted that mmHg is the most used unit in the medical field. All the blood pressure, pulse pressure of a patient is measured in this unit only and it is sought to be the most convenient.