Question

can you please explain
A fuel-air mixture is placed in a cylinder fitted with a piston. The original volume is 0.290-L. When the mixture is ignited, gases are produced and 865 J of energy is released. To what volume will the gases expand against a constant pressure of 635 mmHg, if all the energy released is converted to work to push the piston?

Answer 1

Answer : The final volume of will be 10.5 liters.

Explanation :

Formula used :

$w=-p_{ext}dV\\\\w=-p_{ext}(V_2-V_1)$

where,

w = work done  = -865 J = -8.54 L.atm

Conversion used : (1 L.atm = 101.3 J)

$p_{ext}$ = external pressure = 635 mmHg = 0.836 atm

Conversion used : (760 mmHg = 1 atm)

$V_1$ = initial volume of gas = 0.290 L

$V_2$ = final volume of gas = ?

Now put all the given values in the above formula, we get :

$w=-p_{ext}(V_2-V_1)$

$-8.54L.atm=-(0.836atm)\times (V_2-0.290)L$

$V_2=10.5L$

Therefore, the final volume of will be 10.5 liters.