Nitrogen at an initial state of $$10$$ bar, $$1{m^3}$$ and $$300$$ $$K$$ is expanded isothermally to a final volume of $$2{m^3}$$. The $$p$$-$$v$$-$$T$$ relation is $$\left( {p + {a \over {{v^2}}}} \right)v = RT,$$ where $$a>0.$$ The final pressure

A vertical cylinder with a freely floating piston contains $$0.1$$ $$kg$$ air at $$1.2$$ bar and a small electrical resistor. The resistor is wired to an external $$12$$ Volt battery. When a current of $$1.5$$ amps is passed through the resistor for $$90$$ $$secs,$$ the piston sweeps a volume of $$0.01$$ $${m^3}.$$ Assume $$(i)$$ piston and the cylinder are insulated and $$(ii)$$ air behaves as a ideal gas with $${C_v} = 700\,\,J/kg\,K.$$
Find the rise in temperature of air.