A column of liquid is found to expand linearly on heating. Assume the column rises 5.25 cm for a 10.0°F rise in temperature. If the initial temperature of the liquid is 93.9°F, what will the final temperature be in °C if the liquid has expanded by 19.3 cm?

The mass of a hot-air balloon and its cargo (not including the air inside) is 200 kg. The air outside is at 10.0C and 101 kPa. The volume of the balloon is 400 m3. To what temperature must the air in the balloon be warmed before the balloon will lift off? (Air density at 10.0C is 1.244 kg/m3.)

A cylinder with a piston holds 0.50 m3 of oxygen at an absolute pressure of 4.0 atm. The piston is pulled outward, increasing the volume of the gas until the pressure drops to 1.0 atm. If the temperature stays constant, what new volume does the gas occupy? (a) 1.0 m3 (b) 1.5 m3 (c) 2.0 m3 (d) 0.12 m3 (e) 2.5 m3

A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0C. It is completely filled with turpentine at 20.0C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0C. (a) How much turpentine overflows? (b) What is the volume of the turpentine remaining in the cylinder at 80.0C? (c) If the combination with this amount of turpentine is then cooled back to 20.0C, how far below the cylinders rim does the turpentines surface recede?

A mercury thermometer is constructed as shown in Figure P16.53. The Pyrex glass capillary tube has a diameter of 0.004 00 cm, and the bulb has a diameter of 0.250 cm. Find the change in height of the mercury column that occurs with a temperature change of 30.0C.

Two cylinders A and B at the same temperature contain the same quantity of the same kind of gas. Cylinder A has three times the volume of cylinder B. What can you conclude about the pressures the gases exert? (a) We can conclude nothing about the pressures. (b) The pressure in A is three times the pressure in B. (c) The pressures must be equal. (d) The pressure in A must be one-third the pressure in B.

A liquid with a coefficient of volume expansion just fills a spherical shell of volume V (Fig. P16.53). The shell and the open capillary of area A projecting from the top of the sphere are made of a material with an average coefficient of linear expansion . The liquid is free to expand into the capillary. Assuming the temperature increases by T, find the distance h the liquid rises in the capillary.

A sample of a solid substance has a mass m and a density 0 at a temperature T0. (a) Find the density of the substance if its temperature is increased by an amount T in terms of the coefficient of volume expansion . (b) What is the mass of the sample if the temperature is raised by an amount T?

One way to cool a gas is to let it expand. When a certain gas under a pressure of 5.00 106 Ha at 25.0C is allowed to expand to 3.00 times its original volume, its final pressure is 1.07 106 Pa. (a) What is the initial temperature of the gas in Kelvin? (b) What is the final temperature of the system? (See Section 10.4.)

A spherical shell has inner radius 3.00 cm and outer radius 7.00 cm. It is made of material with thermal conductivity k = 0.800 W/m C. The interior is maintained at temperature 5C and the exterior at 40C. After an interval of time, the shell reaches a steady state with the temperature at each point within it remaining constant in time. (a) Explain why the rate of energy transfer P must be the same through each spherical surface, of radius r, within the shell and must satisfy dTdr=P4kr2 (b) Next, prove that 5dT=P4k0.030.07r2dr where T is in degrees Celsius and r is in meters. (c) Find the rate of energy transfer through the shell. (d) Prove that 5TdT=1.840.03rr2dr where T is in degrees Celsius and r is in meters. (e) Find the temperature within the shell as a function of radius. (f) Find the temperature at r = 5.00 cm, halfway through the shell.