Fifteen joules of heat are added to a cylinder with a piston. the system uses 7 joules of energy to raise the piston upward. by how much did the internal energy of the system increase?

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The starship enterprise is caught in a time warp and spock is forced to use the primitive techniques of the 20th century to determine the specific heat capacity of an unknown mineral. the 125-g sample was heated to 96.3°c and placed into a calorimeter containing 85.9 g of water at 20.0°c. the heat capacity of the calorimeter was 14.2 j/k. the final temperature in the calorimeter was 24.5°c. what is the specific heat capacity (in j/g°c) of the mineral? enter to 4 decimal places.

You are still fascinated by the process of inkjet printing, as described in the opening storyline for this chapter. you convince your father to take you to his manufacturing facility to see the machines that print expiration dates on eggs. you strike up a conversation with the technician operating the machine. he tells you that the ink drops are created using a piezoelectric crystal, acoustic waves, and the plateau-rayleigh instability, which creates uniform drops of mass m = 1.25 ✕ 10−8 g. while you don't understand the fancy words, you do recognize mass! the technician also tells you that the drops are charged to a controllable value of q and then projected vertically downward between parallel deflecting plates at a constant terminal speed of 20.0 m/s. the plates are ℓ = 2.15 cm long and have a uniform electric field of magnitude e = 6.40 ✕ 104 n/c between them. noting your interest in the process, the technician asks you, "if the position on the egg at which the drop is to be deposited requires that its deflection at the bottom end of the plates be 0.17 mm, what is the required charge on the drop (in c)? " you quickly get to work to find the answer. (neglect the force of gravity.)