Experiments carried out by french chemists jacques alexandre césar charles and joseph-louis gay-lussac and british physicist lord kelvin determined a quantitative relationship between the volume and temperature of a gas. their data showed that for a container of gas held at constant pressure, the volume and temperature are directly proportional. for example, if you inflate a balloon outdoors with cold air on a cold day and then take it inside, it will expand, and it might even burst. this happens because as the temperature of the air inside the balloon increases, the volume of the balloon increases as well. what is less obvious is the quantitative relation: if the pressure is held constant, then when the temperature is doubled, the volume is doubled as well.

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

Air conditioners not only cool air, but dry it as well. suppose that a room in a home measures 5.0m×9.0m×2.4m . if the outdoor temperature is 30 ∘c and the vapor pressure of water in the air is 85 % of the vapor pressure of water at this temperature, what mass of water must be removed from the air each time the volume of air in the room is cycled through the air conditioner? the vapor pressure for water at 30 ∘c is 31.8 torr.

You charge a parallel-plate capacitor, remove it from the battery, and prevent the wires connected to the plates from touching each other. when you increase the plate separation, what happens to the following quantities?