3. The isothermal compression of 0.3m^3 of air with initial parameters p_(1)=10 bar and t_(1)= 300^circ C produces 500 kJ of heat Determine the final volume V_(2) and the final pressure p_(2)

To solve this problem, we can use the first law of thermodynamics and the ideal gas law.Given information:- Initial volume: - Initial pressure: - Initial temperature: - Heat added: Step 1: Convert the initial temperature to Kelvin. Step 2: Use the first law of thermodynamics to find the change in internal energy. where is the work done by the system.Step 3: Use the ideal gas law to find the final volume and pressure. where is the pressure, is the volume, is the number of moles, is the specific gas constant, and is the temperature.Since the process is isothermal, the temperature remains constant, and the change in internal energy is zero. Substituting the values, we get: Solving for , we get: Now, we can use the ideal gas law to find the final volume and pressure. Since the number of moles and the gas constant remain constant, we can divide the two equations to eliminate and : Substituting the known values, we get: Solving for , we get: Therefore, the final volume is the same as the initial volume, which is , and the final pressure is .