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6E/S&J 20.17. A 3.00 g lead bullet at 30C is fired at a speed of 240 m/s into a large block of ice at 0C, in which it becomes embedded. What quantity of ice melts? 6E/S&J 20.21. In an insulated vessel, 250 g of ice at 0C is added to 600 g of water at 18C. (a) What is the final temperature of the system? (b) How much ice remains when the system reaches equilibrium? 6E/S&J 20.23. A sample of ideal gas is expanded to twice its original volume of 1.00 m3 in a quasi-static process for which P V 2 , with = 5.00 atm/m6, as shown in Figure P20.23. How much work is done on the expanding gas? 6E/S&J 20.27. One mole of an ideal gas is heated slowly so that it goes from the PV state (Pi, Vi) to (3Pi, 3Vi) in such a way that the pressure is directly proportional to the volume. (a) How much work is done on the gas in the process? (b) How is the temperature of the gas related to its volume during this process? 6E/S&J 20.30. A gas is taken through a cyclic process described in Figure P20.30. (a) Find the net energy transferred to the system by heat during one complete cycle. (b) If the cycle is reversed – that is, if the process follows the path ACBA – what is the net energy input per cycle by heat? 6E/S&J 20.31. Consider the cyclic process depicted in Figure P20.30. If Q is negative for the process BC, and if Eint is negative for the process CA, what are the signs of Q, W, and Eint that are associated with each process? 6E/S&J 20.32. A sample of an ideal gas goes through the process shown in Figure P20.32. From A to B, the process is adiabatic; from B to C, it is isobaric, with 100 kJ of energy entering the system by heat. From C to D, the process is isothermal; from D to A, it is isobaric, with 150 kJ of energy leaving the system by heat. Determine the difference in internal energy Eint,B – Eint,A. 6E/S&J 20.33. A sample of an ideal gas is in a vertical cylinder fitted with a piston. As 5.79 kJ of energy is transferred to the gas by heat to raise the temperature, the weight on the piston is adjusted so that the state of the gas changes from point A to point B along the semicircle shown in Figure P20.33. Find the change in the internal energy of the gas. 6E/S&J 20.36. A 1.00-kg block of aluminum is heated at atmospheric pressure such that its temperature increased from 22.0C to 40.0C. Find (a) the work done on the aluminum, (b) the energy added to it by heat, and (c) the change in its internal energy. 6E/S&J 20.39. A 2.00-mol sample of helium gas initially at 300 K and 0.400 atm is compressed isothermally to 1.20 atm. Noting that the helium behaves as an ideal gas, find (a) the final volume of the gas, (b) the work done on the gas, and (c) the energy transferred by heat. 6E/S&J 20.40. In Figure P20.40, the change in internal energy of a gas that is taken from A to C is +800 J. The work done on the gas along the path ABC is –500 J. (a) How much energy must be added to the system by heat as it goes from A through B to C? (b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D? (c) What is the energy exchanged with the surroundings by heat as the cycle goes from C to A along the green path? (d) If the change in internal energy in going from point D to point A is +500 J, how much energy must be added to the system by heat as it goes from point C to point D? 6E/S&J 20.42. A glass window pane has an area of 3.00 m2 and a thickness of 0.600 cm. If the temperature difference between its faces is 25.0C, what is the rate of energy transfer by conduction through the window? 6E/S&J 20.43. A bar of gold is in thermal contact with a bar of silver of the same length and area (Fig. P20.43). One end of the compound bar is maintained at 80.0C, while the opposite end is at 30.0C. When the rate of energy transfer reaches steady state, what is the temperature at the junction? 6E/S&J 20.49. The tungsten filament of a certain 100-W light bulb radiates 2.00 W of light (the other 98 W is carried away by convection and conduction). The filament has a surface area of 0.250 mm2 and an emissivity of 0.950. Find the filament’s temperature (note that the melting point of tungsten is 3683 K). 6E/S&J 20.51. The intensity of solar radiation reaching the top of the Earth’s atmosphere is 1340 W/m2. The temperature of the Earth is affected by the so-called “greenhouse effect” of the atmosphere. That effect makes our planet’s emissivity for visible light higher than its emissivity for infrared light. For comparison, consider a spherical object with no atmosphere, at the same distance from the Sun as the Earth. Assume that its emissivity is the same for all kinds of electromagnetic waves and that its temperature is uniform over its surface. Identify the projected area over which it absorbs sunlight and the surface area over which it radiates. Compute its equilibrium temperature. Chilly, isn’t it? Your calculation applies to (a) the average temperature of the Moon, (b) astronauts in mortal danger aboard the crippled Apollo 13 spacecraft, and (c) global catastrophe on the Earth if widespread fires should cause a layer of soot to accumulate throughout the upper atmosphere, so that most of the radiation from the Sun were absorbed there rather than at the surface below the atmosphere.