A gas contained in a cylinder fitted with a friction-less piston is regarded as the thermodynamic system. Answer the following questions keeping the accepted algebraic sign convention in mind:
(i) Define heat and work for a thermodynamic system.
(ii) State the sign convention for heat and work as used in the First Law of Thermodynamics.
(iii) During a slow compression the surroundings supply 450J of mechanical energy to the gas through the piston, while the gas simultaneously loses 150J of energy to the surroundings in the form of heat. Assign the correct signs to Q and W for the gas and justify each choice in one or two sentences.