You are a new engineer at a company that manufactures gas-filled shock absorbers for racing cars. The chief engineer wants to understand the relation between the gas pressure inside the shock absorber and the compression of the gas. The shock absorbers are essentially piston-cylinder devices that are initially filled with nitrogen gas at 0.345MPa and 20.0 Fahrenheit. When the piston compresses the gas by 20%, the pressure increases to 0.414MPa. You think this is a polytropic compression process. Write and solve a thermodynamics problem to determine the polytropic exponent for this process.