Find work done on an isobaric system

[Feodalherren]

Homework Statement

A 1kg box of Aluminum initially at 22C is warmed at P=1atm so that its T increases to 40C. Find
a) The work done on the system

Homework Equations

W= -∫PdV

The Attempt at a Solution

The pressure is constant at 101,300Pa

D=m/V

So V=m/D

D of Al at room temp = 2700kg/m^3

Therefore

$W= -101,300Pa \frac{1kg}{2700kg/m^{3}}(1+24x10^{-6}(18))^{3}$

Where ΔT=18 and 24x10^-6 is the linear coefficient of expansion of Aluminum.

= -37.6J

Not the right answer, it should be around 48mJ. I can't see what I'm doing wrong here.

 

[ehild]

Work is PΔV. What is the change of volume?

ehild

 

[Chestermiller]

It should be

$W= -101,300Pa \frac{1kg}{2700kg/m^{3}}((1+24\times 10^{-6}(18))^{3}-1)$

because you forgot to subtract the initial volume. Essentially the same result, which retains only the linear term, is:

$W= -101,300Pa \frac{1kg}{2700kg/m^{3}}(3)(24\times 10^{-6}(18))$

Chet

 

[Feodalherren]

Oh yeah I totally missed that. Thanks.