The pressure of an oxygen containing cylinder is 10.3atm.Under same temperature, another oxygen cylinder having 1/3rd volume and has a pressure 1.1 atm Keeping the temperature same, two cylinders are connected, find the total pressure of the system
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Answer:
Let us assume on the contrary that 2 is a rational number. Then, there exist positive integers a and b such that
2=ba where, a and b, are co-prime i.e. their HCF is 1
⇒(2)2=(ba)2
⇒2=b2a2
⇒2b2=a2
⇒2∣a2[∵2∣2b2 and 2b^2=a^2]
⇒2∣a...(i)
⇒a=2c for some integer c
⇒a^2=4c^2
⇒2b^2=4c2[∵2b^2=a^2]
⇒b^2=2c^2
⇒2∣b
From (i) and (ii), we obtain that √2 is a common factor of a and b. But, this contradicts the fact that a and b have no common factor other than 1. This means that our supposition is wrong.
Hence, √2 is an irrational number.
You use Boyle’s Law. Provided temperature is constant, the pressure is directly proportional to volume.
To calculate how much compressed oxygen you have, you need to know the capacity of your cylinder. Let’s call it 10 litres to make the sums easy.
Next, you need to know the pressure in the cylinder. To make the sums easy, let's use kilopascals. Say the pressure is 10,000 kPa.
One atmosphere is about 100 kPa. So your cylinder contains 100 atmospheres of pressure.
If you vent the cylinder to atmosphere, it will release 10 litres x 100 atmospheres, i.e. 1000 litres of oxygen.
This is all easy because oxygen is always a gas in the cylinder. Nitrous oxide is a liquid in the cylinder, which means the gauge pressure represents only the saturated vapour pressure of nitrous oxide, not the contents. If you want to know how much nitrous is in your cylinder, you need to weigh it. The tare weight (the weight of the empty cylinder) is stamped on the neck of the cylinder for this purpose. This is true for other liquefied gases, such as the propane you use for your barbecue.