Question

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?

the answer is 10.5 L

Answer 1

10.5 L

Step-by-step explanation:

From the question,

Work done in pushing the piston back = Energy released by the system = w = - 865 J (- sign as the heat is being released)

The expression for the calculation of work done is shown below as:

`w=-P* \Delta V`

Where, P is the pressure

`\Delta V` is the change in volume

From the question,

`V_1` = 0.290 L

P = 635 mmHg

Also, P (atm) = P (mm Hg) / 760

Pressure = 635 / 760 = 0.8355 atm

So,

`-865\ J=-0.8355* (V_2-0.290)\ atmL`

Also, 1 J = 1/ 101.325 atmL

So,

`\frac {865}{101.325}=0.8355* (V_2-0.290)`

Solving for
`V_2`, we get that:-

`V_2-0.290=10.210`

`V_2 = 10.5\ L`