Question

One mole of CO2(g) is expanding isothermally and reversibly from a volume of 0.100 dm3 to a volume of 100 dm3. Calculate the work in "kJ" of the expansion process if: 1/ the gas is considered real gas. (Hint: use the Van Der Waals equation for real gases to express the pressure in the work equation). 2/ The gas is considered perfect gas. Given: The constants for CO2(g) are: a= 3.59 atm L2/mol2, b= 0.0427 L/mol Answer: a) the expansion work for CO2 as real gas is W = kJ. b) the expansion work for CO2 as perfect gas is W = kJ.

Answer 1

For the real gas following Vander Waals equation, reversible isothermal work done is given by :

`$W= \int P \ dV$`

`$W= \int \left((nR)/(V-nb)-(an^2)/(V^2)\right) dV$`

`$W_(real)=-nRT \ln \left[(V_2-b)/(V_1-b)\right]-an^2\left[(1)/(V_2)-(1)/(V_1)\right]$`

Given :
`$V_1=0.1 \ dm^3$`,
`$$V_2 =100 \ dm^3`

`$a=359 \ atm \ L^2/ mol^2, \ \ b = 0.0427 \ L/mol$`

As T is not given, assuming T = 290 K

`$W_(real) = 0.0823 * 240 \left[ \ln \left((100-0.042)/(0.1-0.0427)\right)\right]-3.59\left[(1)/(100)-(1)/(0.1)\right]$`

`$W_(real)= -183.06+35.864$`

`$W_(real)=-147.196$`

For the perfect gas,

`$W=nRT \ln\left[(V_2)/(V_1)\right] =(1)(0.0823)(290) \ln \left[(100)/(0.1)\right]$`

`$W_(ideal)=169.415$` kJ