Question

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is 42 cm3. If the combustion of this mixture releases 927 J of energy, to what volume (in L) will the gases expand against a constant pressure of 656 torr if all the energy of combustion is converted into work to push back the piston?

Answer 1

Step-by-step explanation:

Relation between work, pressure and volume is as follows.

W =
`-P \Delta V`

where, W = work = -927 J (as energy is released so, work is done by the system)

P = pressure = 656 torr

=
`8.74 * 10^(4)` Pa (as 1 torr = 133.3 Pa)

Initial volume
`(V_(1))` = 42
`cm^(3)`

=
`42 * 10^(-6) m^(3)` (as 1 m = 100 cm)

Hence, calculate the final volume as follows.

W =
`-P \Delta V`

-927 J =
`-8.74 * 10^(4) Pa * (V_(2) - 42 * 10^(-6) m^(3))`

`106.06 * 10^(-4) = V_(2) - 0.42 * 10^(-4)`

`V_(2)` =
`106.48 * 10^(-4) m^(3)`

= 10.6 L (as 1
`m^(3)` = 1000 L)

= 11 L (approx)

Thus, we can conclude that the gases expand 11 L against a constant pressure of 656 torr.