# Work in mechanics and thermodynamics

Hi, I'm new to this forum . I have long been puzzled over the concept of work in thermodynamics. In mechanics work is defined as the integral of of the force and the displacement dot product. So if they are perpendicular , the work is by definition zero.But in thermodynamics it appears fuzzy. To take an example from thermodynamics , a man who climbs a flight of stairs is said to do no work even though from a mechanics point of view the work will be nonzero . I apologize for being wordy as I ' m unfamiliar with Latex

Hi, I'm new to this forum . I have long been puzzled over the concept of work in thermodynamics. In mechanics work is defined as the integral of of the force and the displacement dot product. So if they are perpendicular , the work is by definition zero.But in thermodynamics it appears fuzzy. To take an example from thermodynamics , a man who climbs a flight of stairs is said to do no work even though from a mechanics point of view the work will be nonzero . I apologize for being wordy as I ' m unfamiliar with Latex

We define pressure most commonly by force per area BUT it is also energy per volume. This gives the most common form of work in thermodyamics

dW = PdV

Say you want to push down on an air tight cylinder containing a compressible fluid. This takes energy to accomplish. Some of the energy goes into work that actually compresses the fluid and some goes into heat.

The above equation is not as simple as it appears, however. The P term is determined by the equation of state (ideal, van der Waals, Redlich Kwong, Peng Robinson...) which are commonly approximately by virial equations and can be many characters long.

It's not common or sometimes accurate to express thermodynamic variables as vectors. It doesn't really give any extra information, so it's left in simple scaler form.

Mapes
Homework Helper
Gold Member
To take an example from thermodynamics , a man who climbs a flight of stairs is said to do no work

Who says this? The man has increased his potential energy by moving upwards against the force of gravity. That's work in my book.

Date of OP ?

.// I have long been puzzled over the concept of work in thermodynamics. In mechanics work is defined as the integral of of the force and the displacement dot product. // But in thermodynamics it appears fuzzy.
To take an example from thermodynamics , a man who climbs a flight of stairs is said to do no work even though from a mechanics point of view the work will be nonzero .

Although it is somewhat shocking, I think it must be admitted that 'work' in thermodynamics is fuzzy.
For the man who climbs the stairs, the only energy transfer from the body(system) to the environment is heat (no sweat): no work is done. Chemical energy stored in glucose is (partly) transformed to the potential energy of the same body. There is transformation of one form of energy to another, but the energy stays in the body.

Secondly in case of a system with piston (eg steam engine) no distinction is made between the work done on the inside of the piston and work done on the outside of the piston, due to a strong belief in reversible processes, which assume p(in)=p(out), hence W(in)=w(out). However in the real world there is no such thing as a reversible process.
( This problem is properly dealt with in the attachement in https://www.physicsforums.com/showthread.php?t=338573 )

Third, there is a sign problem (as indicated by mrmiller1 who leaves th minus-sign out of the equation for work). The sign convention of mechanics is sometimes at odds with the sign convention of thermodynamics.