Question

a steel cylinder of 80 liter capicty contains a gas under a preesure of 200 atm . how many cylinder of 800ml capacity ( at constant temperature) can be filled from it at pressure of 76 cm[ solve and send it. I'll mark you as brainlist]

Answer 1

Boyle's Law states that the volume of a gas is inversely proportional to the pressure at constant temperature.

$\displaystyle\longrightarrow\sf{V\propto\dfrac {1}{P}}$

Therefore,

$\displaystyle\longrightarrow\sf{\dfrac {V_2}{V_1}=\dfrac {P_1}{P_2}}$

$\displaystyle\longrightarrow\sf{V_2=V_1\times\dfrac {P_1}{P_2}}$

Here,

• $\displaystyle\sf {V_1=80\ L}$

• $\displaystyle\sf {P_1=200\ atm}$

• $\displaystyle\sf {P_2=76\ cm\,Hg=1\ atm}$

Then,

$\displaystyle\longrightarrow\sf{V_2=80\times\dfrac {200}{1}}$

$\displaystyle\longrightarrow\sf{V_2=16000\ L}$

$\displaystyle\longrightarrow\sf{V_2=16000000\ mL}$

So the no. of containers each of volume 800 mL filled is,

$\displaystyle\longrightarrow\sf{n=\dfrac {16000000}{800}}$

$\displaystyle\longrightarrow\sf{\underline {\underline {n=20000}}}$