## How do you know which variables in an equation are constant?

How do you know which variables in an equation are constant?

My solution: I think that variables in an equation with no $$\Delta$$ in front of it will be assumed that it is constant always. Is this correct for any equation?

But for PV=nRT, it is kind of ambiguous. Should the problem should always tell you what is constant and what isn't? Like it the problem said the temperature changes, it must also say that either Pressure changes or Volume changes or what you need to solve for right?
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 Also, no object can do negative work right? Work is always positive? I'm confused on the equation: $$W=P\Delta V$$ When the system does work on the environment it is positive and the work done on the system by the environment is negative??

PV=nRT is an equation of state.

http://www.grc.nasa.gov/WWW/K-12/airplane/eqstat.html

http://en.wikipedia.org/wiki/Equation_of_state
 In physics and thermodynamics, an equation of state is a relation between state variables.[1] More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions. It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy.
from the wikipedia article

[1] Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6. cited in the wikipedia article.

But systems can transition from one state to another, depending on various mechanisms, e.g. heat transfer or work, or mass flow.

Work can be done by a system or on a system - as in expansion or compression. And heat can flow into or out of a system depending of course on the temperature difference (gradient).

## How do you know which variables in an equation are constant?

Great post! I don't really understand what is happening when my text says "the work done on the environment by the gas." How does the gas do work on the environment other than that the volume of gas increases. Can you visualize this by thinking of a piston moving upwards and "pushing" on the atmospheric pressure that is directed downwards? Are these forces done to compress and expand the gas external forces or can a gas actually do this by itself. Btw, I'm only referring to the equation W=PV so temperature shouldn't change right?