Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is 35 cm3. If the combustion of this mixture releases 775 J of energy, to what volume will the gases expand against a constant pressure of 710. torr if all the energy of combustion is converted into work to push back the piston

The gases will expand 8.2 L against the constant pressure of 710 torr.

Explanation:

Given that:

the original volume V₁ = 35 cm³ = 35 × 10⁻⁶ m³

Since the combustion of the mixture releases energy then :

the work W = - 775 J

Pressure = 710 torr

Since 1 torr = 133.322 Pa

710 torr = 94658.62 Pa

We all know that:

W = -PdV

-775 = - 94658.62 Pa ( V₂ - V₁ )

-775 = - 94658.62 ( V₂ - 35 × 10⁻⁶)

-775/ - 94658.62 =  V₂ - 35 × 10⁻⁶

0.008187 = V₂ - 35 × 10⁻⁶

V₂ = 0.008187 + 35 × 10⁻⁶

V₂ = 0.008222 m³

The change in volume dV = V₂ - V₁

The change in volume dV = 0.008222 m³ - 35 × 10⁻⁶ m³

The change in volume dV = 0.008187   m³

To litres

The change in volume dV = 8.2 L

Thus, the gases will expand 8.2 L against the constant pressure of 710 torr.

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