[Physics] the difference between work done and energy transfer

energythermodynamicswork

I understand that work done is a form of energy transfer, but I am I right in thinking that energy can be transferred without work being done?

If so, what is it that makes the two different. In particular, in the case of thermodynamics, what is the difference between simply transferring energy to a gas (such as heating) and actually doing work on the gas.

Thanks.

Best Answer

In thermodynamics, work is the negative of the change in internal energy due to a change in volume, usually holding entropy and particle numbers constant. This takes the form of a force pushing on the walls of the volume, which connects it to our conventional notion of work, $W = F~\Delta x$, as seen for example if we consider a cylinder of cross-section $A$, $$W = F~\Delta x = F~\frac AA~\Delta x = \frac FA~A\Delta x = P ~\Delta V.$$And the change in internal energy is just the negative of the work, $-P~\Delta V,$ due to the law of energy conservation.

In fact we can also define that $W = P~\Delta V$ even when we are not holding entropy and particle numbers constant: but then it is not necessarily the same as the change in internal energy. So for example if you compress an ideal gas it generally heats up; you could still speak of the work as $P~\Delta V$ at constant temperature, but "at constant temperature" means essentially "we squeeze this thing and it wants to become warmer, but we let energy out of the system through the walls until it comes back to the same temperature": there has been a negative work, and perhaps the internal energy has still gone up, but it has not gone up as much as it would have had the walls been thermodynamic insulators. In these cases however we can often define a "free energy" (in this case $E - T S$) which the work is the negative of the change of.

Related Question