how do i get 1 atm / (meter^3) to Joules?

Question

I know this1 atm / (meter^3) = 101 325 m^-4 kg s^-2


but Joules is 1 atm / (meter^3) = 101 325 m^4 kg s^-2

I am finding work under a graph that is y=atm and x=m^3 and I found the area to be 1.375 atm/m^3 but I need it in Joules!

Answer 1

Do not go nuts with units. They will dry you batty. Concentrate on concepts
keep in mind that
Work done = (pressure) x( change in volume).
so if say y- pressure and x is volume then the are bounded by x-axis from X1 to X2 is the work done.

more

1 atmosphere[technical] = 98 066.5 Newton/square Meter
but
1 atmosphere [standard] = 101 325.01 newton/square meter (as you have said)
1 Joule = 1 Newton x Meter

so
for standard
Work = 1.375 atm/m^3 [101 325.01 N/m^2]/atm=
=139,322 Joules
for technical
Work=1.375 atm/m^3 [98 066.5 N/m^2]/atm=
=134,841 Joules

Answer 2

Easy. First note that Joules is _not_
Joules = 1 atm / (meter^3) = 101 325 m^4 kg s^-2

The correct expression for Joules is
J = m^2 kg s^-2.

The first expression, however is correct:
1 atm = 101 325 m^-1 kg s^-2,
1 = 101 325 m^-1 kg s^-2 / atm

Take your result
WORK = 1.375 atm * m^3
and mutliply it by the above written expression for 1
(multiplying something by 1 cannot change the reusult, can it?):
WORK = 1.375 atm * m^3 * 101 325 m^-1 kg s^-2 /atm
= 139322 m^2 kg s^-2
= 139.3 kJ