How can an EXPANSION of a gas be ISOTHERMAL??? Isn't that an oxymoron?

Question

Physical chemistry book gives an example of a closed system of gas being heated, but then expanding a piston outward in a cylinder, performing work on the surroundings. It uses this as an example of an isothermal expansion (stating that isothermal means temp of gas is same initial and final). My understanding: But if PV=nRT, and n is UNchanged, then an increase in V (from heating) must be accompanied by an increase in T!!!

It says "so, in conclusion, the total energy of the gas is the same before and after the expansion. Energy has left the system as work; therefore, a compensating amount of energy must have entered the system as heat."

IT SAYS THAT ENERGY ENTERED THE SYSTEM AS HEAT, but then calls this "isothermal." what???

Answer 1

Heat is energy. Temperature is a state. Its confusing because normally heat energy is used to change a temperature state, but this is not always true. That's the concept that you need to grasp. While not exactly what I'd consider practical since the heat/temperature scenario is more common, the emphasis is that you can have an isothermal system, but any energy put into it would require changes in pressure and volume to compensate and maintain the isothermal condition.

The concept is important when you get into the various thermodynamic cycles.

Answer 2

Isothermal means at constant temperature. Let there be a cylinder of a perfectly heat-conductive substance, immersed in a fluid at some temperature T. The cylinder contains a gas, which after a time will have also reached temperature T. Now let the piston in the cylinder partially withdraw, slowly, so that the gas expands but absorbs heat through the cylinder walls. This is an isothermal expansion. Contrast this with the same setup except that the cylinder, instead of being a perfect conductor, is a perfect insulator. Then no heat will enter the gas, and as it expands it will cool This is adiabatic expansion.

Answer 3

It's referring to a specific step in the process.

Step 1. Gas enters cylinder as the piston draws it in.
Step 2. Cylinder compresses gas (adds heat and decrease volume).
Step 3. Heat added by spark plug (adds pressure to system).
Step 4. Gas expands to move cylinder (Volume increases and Pressure decreases). - isothermal
Step 5. Exhausted gas leaves cylinder.

The gas is the same temperature before the cylinder moves as it is during the expansion (Step 4).

Actually, your book says closed system and heat added = heat removed so in that case the closed system is isothermal. There is no change in heat over the closed system. In that case, you have to look at it as a whole and not just heat added part.

Answer 4

Isothermal expansion is associated with change in volume and pressure in the ideal gas equation PV = nRT. n and R being constant, T is also constant for isothermal expansion. for gas to expand or increase in volume under isothermal conditions,pressure always decreases.

Thats the point of isothermal expansion, that increase in volume(if from heating) is compensated by decrease in pressure instead of increase in temperature.

Answer 5

The heat input tries to increase the temp.
The volume expansion tries to lessen the temp.

Result: No temp change = isothermal

Answer 6

your ? is just wordplay try reading it again isothermal expansion is as stated ( SORRY LOST CONNECTION ) it refers to the KINETIC energy of the molecules not the volume they occupy think of it as gas expanding and converting heat to mechanical movement ( at the exact rate the heat is produced so no gain at any time )( got it ? ) ( another way is to think of it as the reverse of converting movement to heat - friction being the simplest example )