Question

A mixture of fuel and is injected into a cylinder fitted with a piston. The initial volume is 0.37 L. After the mixture is ignited, gaseous products are formed and 1885 J of energy is released by the reaction. 311 J of the released energy is lost as heat to the surroundings. To what volume would the gases expand against a constant pressure of 1.036 atm, if the remainig energy is converted to work to push the

Answer 1

The gases will expand to a volume of 2.37 L

Step-by-step explanation:

Gases are able to do work when they expand or compress against an external constant pressure.

This work done by gases when they expand or compress against a constant external pressure is known as pressure-volume work or PV work.

The formula for calculating the work done by gases when they compress or expand against a constant pressure is given as W = PΔV

Where ΔV is change in volume given as V2 - V1

Where V2 is final volume, V1 is initial volume

By convention, W can either be negative or positive. When work is done by the system (ΔV > 0), W is negative and when work is done on the system (ΔV < 0), W is positive.

In the gas mixture above, W = PΔV

Remaining energy, W = (1885 - 311) J = 1574 J

P = 1.036 atm = 1.036 × 760 mmHg = 787.36 mmHg

ΔV = V2 - V1

ΔV = V2 - 0.37

1574 = 1.036 (V2 - 0.37)

V2 - 0.37 = 1574/787.36

V2 - 0.37 = 1.999 L

V2 = 1.999 + 0.37

V2 = 2.369 L

Therefore, the gases will expand to a volume of 2.37 L