Answer to Question #283141 in Physics for Kimgcash

Question

The cylinder of a pump has a volume of 25.0 cm3. It is connected to a container of

volume 225 cm3, containing air at atmospheric pressure (100 kPa). The pump draws air

from the atmospheric and pumps it into the container. Assume that the pump stroke is

slow and therefore the temperature of the air in the container remains constant.

Calculate the pressure of the air in the flask after one stroke of the pump adds more air.

Answer 1

Apply the universal gas law keeping in mind the process did not affect the temperature and volume:

$$PV=\dfrac mMRT,\\\space\\ P_1V=\dfrac {m_1}MRT.$$

Divide one by another:

$$\dfrac{P}{P_1}=\dfrac{m}{m_1}=\dfrac{m}{m+\Delta m},\\\space\\ P_1=P\dfrac{m+\Delta m}{m}=P\dfrac{v+\Delta v}{v}=111\text{ kPa}.$$

*We used $m=v\rho.$ Since the density of gas was constant while it was taken from the atmosphere, the density is equal everywhere.