E2A.6(a) A sample of 4.50g of methane occupies 12.7 dm3 at 310 K. (i) Calculate the work done when the gas expands isothermally against a constant external pressure of 200

Torr until its volume has increased by 3.3 dm². (ii) Calculate the work that would be done if the same expansion occurred reversibly. E2A.6(b) A sample of argon of mass 6.56g occupies 18.5 dm3 at 305 K.(i) Calculate the work done when the gas expands isothermally against a constant external pressure of 7.7kPa until its volume has increased by 2.5 dm3.(ii) Calculate the work that would be done if the same expansion occurred reversibly. F=\frac{k T}{2 l} \ln \left(\frac{1+v}{1-v}\right) \quad v=\frac{n}{N} where k is Boltzmann's constant, N is the total number of units, and l= 45 nm for DNA. (a) What is the magnitude of the force that must be applied to extend a DNA molecule with N=200 by 90 nm? (b) Plot the restoring force against v, noting that v can be either positive or negative. How is the variation of the restoring force with end-to-end distance different from that predicted by Hooke's law? (c) Keeping in mind that the difference in end-to-end distance from an equilibrium value is x = nl and, consequently, dx = ldn= Nldv,write an expression for the work of extending a DNA molecule. Hint: You must integrate the expression for w. The task can be accomplished best with mathematical software.