Question

Suppose an ideal gas is in a container 8.0 l in volume and allowed to expand by having a piston move. The final volume after the piston moves is 16.0 l. If the gas is originally at a pressure of 33,000 pa and a temperature of 300.0 k and the temperature is maintained, what will be the new pressure?

Answer 1

the initial condition is given as -

$p_{1}$=33,000 pa

$v_{1}$=8.0 litre i.e 8×$10^{-3}$ $m^{3}$

$t_{1}$ =300k

final state is given as-

$v_{2} =16 litre$ i.e16$*10^{-3}$ $m^{3}$

$p_{2} =?$

$t_{2}$ =300k[the temperature is constant here]

here the temperature is constant.we have to calculate the final pressure

as per the Boyle's law,

                              $p_{1} *v_{1} =p_{2} *v_{2}$

                                       $p_{2} =\frac{p_{1}*v_{1}  }{v_{2} }$

                                                        =$\frac{8*10^{-3}*33000 }{16*10^{-3} }$

                                                         =16500 pa [ans]