$2-48$ A frictionless piston$-$cylinder device contains $10$ kg of water at $20C$ at atmospheric pressure. An external force $F$ is then applied on the piston antil the pressure inside the cylinder increases to $100$ atm $.$ Assuming the coefficient of compressibility of water remains unchanged during the compression; estimate the energy needed to compress the water isothermally. Answer: $244$ J

$2-49$ Reconsider Prob. $2-48.$ Assuming a linear pressure increase during the compression, estimate the energy needed to compress the water isothermally.