Assignment:
Question
1- At a pressure of 0.0500 atm a constant-volume ideal gas thermometer reads a temperature of 345 K. What is the thermometer\'s triple point pressure, Pt?
For the same ideal gas thermometer what temperature, T, corresponds to a pressure of 0.00560 atm?
2- The storage of radioactive waste is an important problem in the nuclear industry. One problem that scientists must take into account is volumetric expansion. Consider a 30.0-gallon metal canister of diameter 22.0 inches filled with a radioactive waste possessing a coefficient of volume expansion of 9.60 × 10-4 (°C)-1. This canister will be filled at room temperature (23.0°C) and lowered deep into the Earth (where temperatures can reach 138°C) for storage. If the coefficient of volume expansion of the metal is 4.10 × 10-5 (°C)-1, how much waste will spill over the top if the lid becomes loose?
3- Volumetric expansion coefficients of simple materials are often well catalogued. However, the thermal expansion coefficient β of a human body is less well known. This could affect the human body\'s specific gravity and, therefore, measurements of its body/fat ratio. Suppose that a human body of weight w0 (on dry land) is placed on a scale while completely immersed in formaldehyde of temperature T1. Once the temperature increases by ΔT, the scale reading drops by Δw.
Derive an expression for β in terms of ΔT, w0, and Δw by assuming that the ratio of the formaldehyde ρf and the initial density of the body ρb is R = ρf /ρb. Assume also that ρf does not change when heated.
If the body weighs 198.5 lb on dry land and his weight reading lowers by 0.237 lb when the formaldehyde is heated from 69.20oF to 82.80oF, calculate the coefficient of volume expansion of the body. Assume R = 0.870.
The coefficient β will likely vary widely from one human body to the next. The numerical value computed here should not be considered factual.
4- As an accountant in charge of reducing expenditures for a local company, you think you can save considerable money on fuel costs by lowering the room temperature of the building for daily use. In the morning, the interior temperature is typically 37.6°F and the thermostat is typically set for 71.4°F. Instead, you propose to lower the thermostat to 60.7°F. Currently the building measures 23.5 × 54.9 × 14.5 feet. How much heat will be saved each morning by bringing the building up to the new operating temperature of 60.7°F instead of 71.4°F? Ignore heat and air losses to the outside and consider air an ideal diatomic gas. Assume that in the morning the pressure in the room is atmospheric. Express your answer as a positive quantity.
The electricity rate in your area is $6.56 per kilowatt-hour. How much money (in dollars) is saved each morning by only heating the room to the new operating temperature?
This represents only a fraction of the cost savings, since higher interior temperatures induce higher losses of heat to the outside.
5- A uniform steel plate has an area of 0.919 m2. When subjected to a temperature difference between its sides, a heat current of 37.5 kW is found to flow through it. What is the temperature gradient? What is the temperature difference when the plate is 4.35 cm thick? The thermal conductivity of steel is 50.2 W/(m•K).
Temperature gradient:
Temperature difference:
6- Temperatures of gases inside the combustion chamber of a four stroke automobile engine can reach up to 1000°C. To remove this enourmous amount of heat the engine utilizes a closed liquid cooled system which relies on conduction to transfer heat from the engine block into the liquid and then into the atmosphere by flowing coolant around the outside surface of the cylinder. Let\'s assume we have a 6 cylinder engine and each cylinder has a diameter of 8.25 cm and height of 11.9 cm and is 3.78 mm thick.
The temperature on the inside of the cylinders is 188.4°C whereas the temperature where the coolant passes is 134.2°C. The temperature of the liquid (a mixture of water and antifreeze) is to be maintained at 95.0°C. Using the given parameters, what flow rate would need to be supplied by the water pump to cool this engine?
7- Find the net rate of radiation by a pot at 38.5°C that has been placed in a -22.7°C freezer. The pot\'s surface area is 0.111 m2 and its emissivity is 0.545.