A piston has an external pressure of 10.0 atm . How much work has been done in joules if the cylinder goes from a volume of 0.140 liters to 0.470 liters?

Question

The joule (JJ) is a unit of energy. Recall that energy may be converted between many different forms such as mechanical energy, thermal energy (heat), chemical energy, electrical energy, and light.

The mechanical energy produced by a system is called work. When work is accomplished through the changing volume of a gas, it is called PV work and is given by the formula w=−PΔVw=−PΔV, where www is the work, PPP is the external pressure, and ΔVΔVDeltaV is the change in volume. If the volume change and pressure are in liters and atmospheres respectively, then the work will have units of liter-atmospheres, which can be converted to joules using the conversion factor 1 L⋅atm=101.3 J1 L⋅atm=101.3 J.

Work can also be expressed as force multiplied by distance: w=F×dw=F×d, where www is the work in joules, FFF is the force in newtons, and ddd is the distance in meters. Note that 1 N⋅m=1 J1 N⋅m=1 J.

Answer 1

w = -P∆V

w = work = ?

P = pressure = 10.0 atm

∆V = change in volume = 0.470 L - 0.140 L = 0.330 L

w = -(10.0 atm)(0.330L)

w = -3.30 Latm

Converting this to joules we have ...

-3.30 Latm x 101.3 J / Latm = -334 J