Question

A cylinder is filled with 10.0 L of gas and a piston is put into it. The initial pressure of the gas is measured to be 163 kPa. The piston is now pushed down, compressing the gas, until the gas has a final volume of 4.40 L.

a) Calculate the final pressure of the gas. Round your answer to 3 significant digits.

Answer 1

The final pressure of the gas is 370. kPa

Step-by-step explanation:

Let's assume the gas inside cylinder behaves ideally.

As amount of gas remains constant in both state therefore in accordance with combined gas law for an ideal gas-

`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`

where
`P_(1)` and
`P_(2)` are initial and final pressure respectively.

`V_(1)` and
`V_(2)` are initial and final volume respectively.

`T_(1)` and
`T_(2)` are initial and final temperature in kelvin scale respectively.

Another assumption is necessary to solve this problem which is the process should be isothermal.

So
`T_(1)=T_(2)` ,
`V_(1)=10.0L` ,
`P_(1)=163kPa` and
`V_(2)=4.40L`

Hence
`P_(2)=(P_(1)V_(1))/(V_(2))`

`\Rightarrow P_(2)=((163kPa)* (10.0L))/(4.40L)`

`\Rightarrow P_(2)=370.kPa`

So the final pressure of the gas is 370. kPa