Chemistry mass balance question

Question

A cylinder with a movable piston contains 4 L of a gas held at 300K and 500kPa. The piston is slowly moved to compress the gas to 800 kPa.

(a) Write the energy balance equation with any simplifications you deem necessary. No assume that the process is isothermal.

(b) Suppose the compression process is performed isothermally and the compression work equals 675 J. If the gas is ideal, calculate the amount of heat exchanged with the surroundings.

(c) Suppose the process is adiabatic. The final temperature of the gas will be equal to, higher or lower than the what 300K?

Answer 1

Hi Marcelo Jr. M.,

This is not a mass balance problem, it's thermodynamics (heat and movement!).

So -- when you compress the gas, you are accelerating (providing internal energy) the molecules. Beyond that, you would need to know, is it a monatomic gas (e.g., He), a diatomic gas (e.g. N₂ ), or a gas with molecules with 3-D rotational possibilities (calculating for vibrations is a whole different ball-game, I think).

So assume monatomic, then you have only 3 degrees of translational kinetic energy to deal with. Otherwise, some energy gets siphoned off into rotational motion, which you must "fill".

For (a), you can't say about energy, without knowing whether or not you withdraw heat to maintain isothermal conditions! The change in P*V will depend; you know deltaP but deltaV is not calculated without a constraint (as in (b) or (c).

For (b), now you can calculate Vfinal from Pfinal, thus you know delta(PV) and the work put in. The difference is heat out!

For (c), adiabatic, you know the work put in from (b). Part of that was delta(PV) work, and part went into a temperature increase. You may find the equation for PV adiabatic changes for a monatomic gas (it has a different exponent than 1 on one of the variables), and apply it.

-- Cheers, --Mr. d.