Consider a cylinder filled with air with a piston and spring arrangement on top. 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 50 cm and the spring constant is 40,000 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 2 cm. You can treat the air as an ideal gas and assume that deltau is given by the product of the constant volume heat capacity and deltaT.