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Can someone help and give me steps to these gas law equations?

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1. I've got the answer but I'm not sure about the method?

A gas cylinder has a volume of 0.024m3 and is fitted with a valve designed to release the gas if the pressure of the gas reaches 115kPa.

Calculate the pressure on the cylinder of this amount of gas at 8oC.
The molar gas constant has a value of 8.31 J mol-1 K-1. At Standard Temperature and Pressure (STP) 1 mole of any gas has a volume of 0.024m^3

At the start of a journey the pressure of the air in a car tyre is 180 kPa and the temperature is 18oC. After being driven the pressure is 303 kPa. Assuming that the volume of the air remains constant what is its temperature now?

The volume of a fixed mass of gas at 15oC was 0.078 m^3. The gas was then heated to 45oC without change of pressure.

Calculate the new volume of this gas.

i) A mass of gas occupies a volume of 200 cm^3 at a temperature of
27oC and a pressure of 1 atmosphere. Calculate the volume when:
a) The pressure is doubled at constant temperature
b) The absolute temperature is doubled at constant pressure
c) The pressure is 1.5 atmospheres and the Celsius temperature is 127oC
2. (Original post by mrpopodopalaus)

A gas cylinder has a volume of 0.024m3 and is fitted with a valve designed to release the gas if the pressure of the gas reaches 115kPa.

Calculate the pressure on the cylinder of this amount of gas at 8oC.
The molar gas constant has a value of 8.31 J mol-1 K-1. At Standard Temperature and Pressure (STP) 1 mole of any gas has a volume of 0.024m^3

At the start of a journey the pressure of the air in a car tyre is 180 kPa and the temperature is 18oC. After being driven the pressure is 303 kPa. Assuming that the volume of the air remains constant what is its temperature now?

The volume of a fixed mass of gas at 15oC was 0.078 m^3. The gas was then heated to 45oC without change of pressure.

Calculate the new volume of this gas.

i) A mass of gas occupies a volume of 200 cm^3 at a temperature of
27oC and a pressure of 1 atmosphere. Calculate the volume when:
a) The pressure is doubled at constant temperature
b) The absolute temperature is doubled at constant pressure
c) The pressure is 1.5 atmospheres and the Celsius temperature is 127oC
Ok so all of these questions are about applying the ideal gas law

PV=NRT

P = pressure (Pa)
V = volume (m^3)
N = number of moles
R = universal gas constant (8.314 J/mol/K or 287J/Kg/K for air)
T = Temperature (K - always convert from celsius to kelvin!)

the first question tells you that N = 1 and also tells you that the volume occupied by the gas is fixed. So it becomes a case of rearranging the ideal gas law and plugging in the numbers.

Question 2 is a bit trickier as you don't know the number of moles or the volume but you know both are constant as no air escapes and the tyre has a fixed volume (in reality tyres expand but for the purposes of the question it is fixed).

Therefore set the values at the start and end to etc.

You now have two sets of equations:

Dividing 1 equation through by the other gives that the initial pressure divided by the final pressure is equal to the initial temperature divided by the final temperature.

The third problem is similar to the second but with pressure fixed instead of volume so by dividing the equations you get a slightly different result.

Not sure if latex was working properly so let me know if the equations haven't displayed properly!

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