You have a gas at 25 C confined to a cylinder with a movable
pist...

Question

You have a gas at 25 C confined to a cylinder with a movable
piston. Which of the following actions would double
the gas pressure?
(a) Lifting up on the piston to double the volume while keeping the temperature constant
(b) Heating the gas so that its temperature rises from 25 C to 50 C, while keeping the volume constant 
(c) Pushing down on the piston to halve the volume while keeping the temperature constant.

Accepted Answer

Hi everyone for this problem, we're told to consider a gas and a fixed volume sealed container at 20°C. Which statement below describes a method to reduce the pressure of the gas by half. So let's write down our ideal gas law so that we can reference the variables were being asked about. So we're told that We have a temperature of 20°C and we want to know which method will reduce the pressure Of the gas by one half. So our two variables that we're looking at here is temperature and pressure. And so far we see here that they have a direct relationship. So for option one, it says increasing the gas temperature up to 40°C. 20° our initial, our initial temperature is 20 degrees and Option one, we're doubling that to 40, so from 20 to 40 and so a doubling our temperature because it's a direct relationship to pressure is going to lead to doubling our pressure. Okay, So here we see that if we increase 2 times, then this is going to increase by two times. Okay, that's option one. So that's not going to be the correct answer option to decreasing the gas temperature Up to 10°C. So we're going from 20°C to 10°C. So we're cutting it in half. So if we have our temperature We're decreasing the temperature from 20°C to 10°C. If we have our temperature, that is going to lead to half ng our pressure because as we said, they have a direct relationship, they're directly proportional. So if we just to show you, just to illustrate if we decrease our temperature by one half, it's going to decrease our pressure by one half and that so far is the correct answer because it's asking which method will reduce the pressure of the gas by half. So this one is correct, but let's take a look at the last one adding the same amount of gas as initially present. So the amount of gas initially present. That means we're going to we're not told the amount of gas that's initially present, but if we add the same amount, that means that we're doubling. So for this one we're looking at moles the relationship between moles and pressure. So if we increase our moles by two times, this is going to increase our pressure by two times. Okay, so double our moles is going to equal double our pressure. So as you can see option two is the correct answer by decreasing the gas temperature Up to 10°C, which is half it's going to have our pressure. That's the end of this problem. I hope this was helpful

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