1. Fort Saint Vrain Power plant was first a nuclear power plant that was later converted to use a carbon based fuel (propane). The main water tank is 100,000 liters which is draws from the Platte river. Consider the water to be at room temperature (293 K). Use the listed energy densities to determine the amount fuel need to boil off the water.
1. Coal 24 MJ/kg 2. Propane 50 MJ/kg
3. Crude oil 46 MJ/kg 4. Refined Uranium 3,456,000 MJ/kg
2. The latest solar technology uses mirrors to redirect sunlight to a tank of liquid graphite that is pumped passed a large tank of water. The graphite is heated to a temperature 5000 k by the redirected sunlight. How much liquid graphite is needed to heat the same tank is used in the previous problem at the same temperature.
3. A precious-stone dealer wishes to find the specific heat capacity of a 0.030-kg gemstone. The specimen is heated to 95.0°C and then placed in a 0.15-kg copper vessel that contains 0.080 kg of water at equilibrium at 25.0°C. The loss of heat to the external environment is negligible. When equilibrium is established, the temperature is 28.5°C. What is the specific heat capacity of the specimen?
4. Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, 0.6 kg of blood flows to the surface of the body and releases 2000 J of energy. The blood arriving at the surface has the temperature of the body interior, 37.0°C. Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.
5. When resting, a person has a metabolic rate of about 4.2 X 10⁵ joules per hour. The person is submerged neck-deep into a tub containing 1.0 X 10³ kg of water at 27.00 °C. If the heat from the person goes only into the water, find the water temperature after half an hour.
6. In a passive solar house, the sun heats water stored in barrels to a temperature of 38 °C. The stored energy is then used to heat the house on cloudy days. Suppose that 2.4 X 10⁸J of heat are needed to maintain the inside of the house at 21 °C. How many barrels (1 barrel = 0.16 m³) of water are needed?
7. An electric hot water heater takes in cold water at 13.0 °C and delivers hot water. The hot water has a constant temperature of 45.0 °C, when the "hot" faucet is left open all the time and the volume flow rate is 5.0 X 10-6 m³/s. What is the minimum power rating of the hot water heater?
8.The supersonic aircraft Concorde has a length of 62.0 m when sitting on the ground on a typical day when the temperature is 18.0 Celsius. The Concorde is primarily made of aluminum. In flight at twice the speed of sound, friction with the air warms the Concorde's skin and causes the aircraft to lengthen by 29.0 cm. (The passenger cabin is on rollers, so the airplane expands around the passenger cabin.) Take the coefficient of linear expansion for aluminum to be = 2.40×10-5 m/K. What is the temperature of the Concorde's skin in flight?
9. How much taller is the Eiffel Tower on the hottest day of the summer (25 ℃) than the coldest day of the winter (2 ℃)? The tower is 324 m tall measured from the top of the flagpole. Assume the tower is built of structural steel. (It's actually made of "puddle iron".)
10. Due to the high specific heat and low conductivity of water, only the uppermost 10% of the oceans is able to undergo any significant temperature change.
a. The natural variation in ocean levels is about 10 cm from September to March. By how much does the mean temperature of the upper ocean change during this time?
b. Global warming is likely to cause a rise in sea level for a number of reasons, one of which is the thermal expansion of water. Determine the rise in sea level for every 1.0 C° temperature increase in the upper ocean.
surface area 3.61 × 1014 m2 mean depth 3794 m
mean temperature, overall 3.5 ℃ mean temperature, top 10% 10 ℃
11. A blimp in the shape of Mr. McNeill contains 5400m³ of helium (He) at an absolute pressure of 1.1 x 10⁵ Pa. The temperature of the He is 280K. What is the mass in kg of the He in the McNeill Blimp?
12. Oxygen for hospital patients is kept in special tanks, where the oxygen has a pressure of 65.0 atmospheres and a temperature of 288K. The tanks are stored in a separate room and the oxygen is pumped to the patient's room, where it is administered at a pressure of 1.00 atmospheres and a temperature of 297K. What volume does 1.00m³ of oxygen in the tanks occupy at the conditions of the patients room?
13. On the sunlit surface of Venus, the atmospheric pressure is 9.6 x 10⁶ Pa, and the temperature is 740K. On the Earth's surface the atmospheric pressure is 1.0 x 10⁵ Pa, while the surface temperature can reach 320K. These data imply that Venus has a 'thicker' atmosphere at its surface than does Earth, which means the number of molecules per unit volume (NIV) is greater on the surface of Venus than on Earth. Find the ratio of (NIV) Venus to (NIV) Earth.
14. Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is 5.6 x 10⁵ m³, and the pressure of the air in the cavern is 7.7 x 10⁶ Pa. Assume that air is a diametric ideal gas whose internal energy U is given by U=5/2nRT. If one home uses 30.0kW•h of energy per day, how many homes could this internal energy serve for one day?