For all questions involving calculations, write out any equations used in the solution. (a) A bottle has a volume of 125cm3. It contains compressed monatomic ideal gas held at 12.0 bar and 293K. The external pressure is exactly 1 bar. (i) Explain why the U=0 for any isothermal process involving an ideal gas. (ii) Calculate the value for work ( w ) for the system if the can is vented irreversibly until equilibrium. (iii) If the system expanded adiabatically, calculate the temperature change of the system from this process. Assume the heat capacity of the system is (3/2)nR. (b) (i) Derive the formula for the constant-volume heat capacity of a substance (CV). Start from U=q+w. Assume that the only source of work is reversible expansion work. (ii) Derive the formula for the constant-volume heat capacity of a substance (Cp). Start from H=U+pV. Assume that the only source of work is reversible expansion work. (iii) Explain why CV for a monatomic ideal gas is (3/2)R. (iv) Use the definitions of Cp and H and the ideal gas law to show that Cp for a monatomic ideal gas is CV+R