Consider a cylinder filled with air with a piston and spring arrangement on top. The spring is 55 cm with the piston loaded, the diameter of the cylinder is 30cm and the height compressed is 15cm. The external pressure is 1 bar, the initial temperature of the air in the cylinder is 25 C. The no-load length of the spring is 50cm and the spring constant is 40000 N/m. The piston weighs 500 kg. You can assume the constant volume heat capacity of air to be constant at 20.9 J/(mol K). a. Compute the initial pressure of the gas in the cylinder. b. Compute how much heat must be added to the gas in the cylinder for the spring to compress by 2cm. You can treat the air as an ideal gas and assume that delta u is given by the product of the constant volume heat capacity and delta T.