Solve: For the copper can, For the water, For the ice, For the lead, gives which confirms that all the ice melts. 14.77. Set Up: The magnitude of the gravitational potential energy change, mgh , equals the heat Q that goes into the ice. Solve: 14.78. Set Up: Kinetic energy is where m is the mass of the spacecraft. Solve: (a) (b) Unless the kinetic energy can be converted other forms than the increased heat of the spacecraft, the satellite can-not return intact. 14.79. Set Up: The mass if air in the room is Solve: (a) (b) (c) 14.80. Set Up: At the sample is at its melting point and at all the sample has melted. Solve: (a) It takes 1.5 min for all the sample to melt once its melting point is reached and the heat input during this time interval is (b) The liquid’s temperature rises in 1.5 min. The solid’s temperature rises in 1.0 min. 14.81. Set Up: For water, If the final temperature is all the ice melts and all the steam condenses. 30.0°C, L v 5 2.256 3 10 6 J / kg. L f 5 3.34 3 10
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