An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant

Q. An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is______cal. (Round off to two decimal places)

(Gas constant R = 0.082 L atm mol^–1 K^–1 = 2 cal mol^–1 K^–1)

Solution:

Ideal Gas Equation- PV= n RT,  where P = Pressure, V = Volume, n = No. of moles, R = Gas constant, T = Temperature. 

Given, P1 = 12 atm , V1 = V (L), Pext = 2 atm, V = 2L .

Using,

PV = n RT,

V = RT/ P where n is unity and T = 298 K . 

W = -Pext (V2 – V1) ,

W = -2 atm  (3L – RT1 / P1),  

W = -2 atm (3L – 0.082Latm K-1mol-1 x 298 K / 12 atm ),  

W = -1.927 atm L, Using 1 atm L = 101.32 J,  

W = -1.927 x 101.32 / 4.184  calories.  

W = -46.66 calories.