G (12 points) The time between incoming phone calls at a call center is a random variable with exponential density p(x) = 1 r e −x/r on [0, [infinity]), where r = 20 ln(2). a. Verify that the function p(x) is a Probability Density Function.

Air is contained in a variable-load piston-cylinder device equipped with a paddle wheel. initially, air is at 400 kpa and 17°c. the paddle wheel is now turned by an external electric motor until 75 kj/kg of work has been transferred to air. during this process, heat is transferred to maintain a constant air temperature while allowing the gas volume to triple. calculate the required amount of heat transfer in kj/kg.