2 8 marks Prof Saha gave the following problem to four

Last updated: 6/24/2023

2 8 marks Prof Saha gave the following problem to four students In this problem work done by a system on its surroundings is taken as positive A non ideal gas follows the Van der Waals equation of state P V nb nRT where P V and T denote the pressure volume and temperature respectively n is the number of moles R is the universal gas constant and a bare dimensional positive constants This gas expands adiabatically from an initial temperature T and volume V to a final temperature Ty and volume V The adiabatic process is described by an equation of the form f P V n a b a constant where a is a dimensionless number which is greater than 1 It is given that a in the ideal gas limit where is the adiabatic exponent What is the work W done by the gas in the process The four students solved the problem independently and gave for different answers Their answers were a W b W nR nR a 1 T T n a V V T T n a V V n R a 1 nR c W d W R T T w T T n a V V 1 Vj nb T 1 1 Vi nb Now Prof Saha had actually provided the exact expression of f P V n a b a to the students but could not remember it during evaluation Still he could determine that some or all of the four answers above must be incorrect based on general physical arguments alone Consider each of the four answers and give at least one reason for each of them showing why it is wrong or possibly correct Note that you are not required to give a correct expression for W or a detailed derivation for it in this question