# How much work is done by the gas?

• Tehy
In summary, the conversation is discussing how to solve an exercise involving 5 moles of gas at a temperature of 326K and a pressure that is expanded from 1atm to 3atm. The question asks how much work is done by the gas. The expert provides a detailed explanation, taking into consideration external pressure changes and heat being added or released. They also mention that if the temperature is kept constant, the work done can be calculated using the formula W = -nRTln(Vi/Vf). However, if the temperature increases due to adiabatic conditions, the calculation is more complicated.

#### Tehy

Hello! Any ideas how I could solve this exercise:

5 mol of gas is in temperature of 326K and the same time the pressure is expanded from 1atm to 3atm. How much work is done by the gas?

Detailed instruction would be good, thanks :)

W/mole = dPV = Pdv + Vdp.

it should be pretty obvious from here.

sicjeff said:
W/mole = dPV = Pdv + Vdp.

it should be pretty obvious from here.

Yes, it probably should, but I'm very dumb with physics :P I already tried to find some help from Google but I didn't have any luck :/

okay, I assume you are in like a freshman/sophmore level physics course right.

Let's assume an ideal gas.

we know the standard molar volume right? (22.414 L/mole). so v=nRT/P.
We are assuming that the size of our container is constant. (isochoric condition)

sicjeff said:
okay, I assume you are in like a freshman/sophmore level physics course right.

Let's assume an ideal gas.

we know the standard molar volume right? (22.414 L/mole). so v=nRT/P.
We are assuming that the size of our container is constant. (isochoric condition)

Oh, yes it's ideal gas. I forget to mention that :)

Do I need to calculate v1= nRT/1atm and then v2= nRT/3atm?

Tehy said:
Hello! Any ideas how I could solve this exercise:

5 mol of gas is in temperature of 326K and the same time the pressure is expanded from 1atm to 3atm. How much work is done by the gas?

Detailed instruction would be good, thanks :)
The question does not have sufficient information. You have to know how the pressure is changed and whether heat is being added or released.

If the external pressure is increased, the volume must decrease, in which case the work done by the gas is negative. If pressure is increased because heat is added, the volume can be held constant, in which case, no work is done. Or it could increase, in which case the work done by the gas is positive.

Work = Pdv not $\Delta (PV)$

If you assume that the external pressure is gradually changed from 1 atm to 3 atm, and the temperature is kept constant, the work done is:

$$W = \int_{P_i}^{P_f} PdV = \int_{P_i}^{P_f} nRTdV/V = nRT\ln(\frac{V_f}{V_i}) = -nRT\ln(\frac{V_i}{V_f})$$

If it is adiabatic (temperature will increase) it is more complicated.

AM

Thanks Andrew! That works great! :)