algebra factoring

Sec. 19-2 â–¡ Thermometers and Temperature Scales1. Fahrenheit and Celsius At what temperature is the Fahrenheit scale reading equal to (a) twice that of the Celsius and (b) half that of the Celsius?2. Oyntyakon (a) In 1964, the temperature in the Siberian village of Oymyakon reached — 71°C. What temperature is this on the Fahrenheit scale? (b) The highest officially recorded temperature in the continental United States was 134°F in Death Valley, California. What is this temperature/on the Celsius scale?Sec. 19-4 â–¡ Heating, Cooling, and Temperature3. Hot and Cold It is an everyday observation that hot and cold objects cool down or warm up to the temperature of their surroundings. If the temperature difference AT between an object and its surroundings (AT = Tobj - Tsur) is not too great, the rate of cooling or warming of the object is proportional, approximately, to this temperature difference; that is,where A is a constant. (The minus sign appears because AT decreases with time if AT is positive and increases if AT is negative.) This is known as Newton's law of cooling, (a) On what factors does A depend? What are its dimensions? (b) If at some instant f, = 0 the temperature difference is Ar1; show that it isat a later time t2.4. House Heater The heater of a house breaks down one day when the outside temperature is 7.0°C. As a result, the inside temperature drops from 22°C to 18°C in 1.0 h. The owner fixes the heater and adds insulation to the house. Now she finds that, on a similar day, the house takes twice as long to drop from 22°C to 18°C when the heater is not operating. What is the ratio of the new value of constant A in Newton's law of cooling (see Problem 3) to the previous value?Sec. 19-5 â–¡ Thermal Energy Transfer to Solids and Liquids5. A Certain Substance A certain substance has a mass per mole of 50 g/mol. When 314 J of thermal energy is transferred to a 30.0 g sample, the sample's temperature rises from 25.0°C to 45.0°C. What are (a) the specific heat and (b) the molar specific heat of this substance? (c) How many moles are present?6. Diet Doctor A certain diet doctor encourages people to diet by drinking ice water. His theory is that the body must burn off enough fat to raise the temperature of the water from 0.00°C to the body temperature of 37.0°C. How many liters of ice water would have to be consumed to burn off 454 g (about 1 lb) of fat, assuming that this much fat burning requires 3500 Cal be transferred to the ice water? Why is it not advisable to follow this diet? (One liter = 103 cm3. The density of water is 1.00 g/cm3.)7. Minimum Energy Calculate the minimum amount of energy, in joules required to completely melt 130 g of silver initially at 15.0°C.8. How Much Unfrozen How much water remains unfrozen after 50.2 kJ of thermal energy is transferred from 260 g of liquid water initially at its freezing point?9. Energetic Athlete An energetic athlete can use up all the energy from a diet of 4000 food calories/day where a food calorie = 1000 cal. If he were to use up this energy at a steady rate, how would his rate of energy use compare with the power of a 100 W bulb? (The power of 100 W is the rate at which the bulb converts electrical energy to thermal energy and the energy of visible light.)10. Four Lightbulbs A room is lighted by four 100 W incandescent lightbulbs. (The power of 100 W is the rate at which a bulb converts electrical energy tff thermal energy and the energy of visible light.) Assuming that 90% of the energy is converted to thermal energy, how much thermal energy is transferred to the room in 1.00 h?11. Drilling a Hole A power of 0.400 hp is required for 2.00 min to drill a hole in a 1.60 lb copper block, (a) If the full power is the rate at which thermal energy is generated, how much is generated in Btu?_(b) What is the rise in temperature of the copper if the copper absorbs 75.0%-of this energy? (Use the energy conversion 1 ft- lb = 1.285 X lO^Btu.)12. How Much Butter How man^ grams of butter, which has a usable energy content of 6.0 Cal/g (= 6000 cal/g), would be equivalent to the change in gravitational potential energy of a 73.0 kg man who ascends from sea level to the top of Mt. Everest, at elevation 8.84 km? Assume that the average value of g is 9.80 m/s2.13. Immersion Heater A small electric immersion heater is used to heat 100 g of water for a cup of instant coffee. The heater is labeled "200 watts," so it converts electrical energy to thermal energy that is transferred to the water at this rate. Calculate the time required to bring the water from 23°C to 100°C ignoring any thermal energy that transfers out of the cup.14. T\ib of Water One way to keep the contents of a garage from becoming too cold on a night when a severe subfreezing temperature is forecast is to put a tub of water in the garage. If the mass of the water is 125 kg and its initial temperature is 20°C, (a) how much thermal energy must the water transfer to its surroundings in order to freeze completely and (b) what is the lowest possible temperature of the water and its surroundings until that happens?15. A Chef A chef, on finding his stove out of order, decides to boil the water for his wife's coffee by shaking it in a thermos flask. Suppose that he uses tap water at 15°C and that the water falls 30 cm each shake, the chef making 30 shakes each minute. Neglecting any transfer of thermal energy out of the flask, how long must he shake the flask for the water to reach 100°C?16. Copper Bowl A 150 g copper bowl contains 220 g of water, both at 20.0°C. A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100°C. Neglect energy transfers with the environment, (a) How much energy (in calories) is transferred to the water? (b) How much to the bowl? (d) What is the original temperature of the cylinder?17. Ethyl Alcohol Ethyl alcohol has a boiling point of 78°C, a freezing point of -114°C, a heat of vaporization of 879 kJ/kg, a heat of fusion of 109 kJ/kg, and a specific heat of 2.43 kJ/kg • C°. How much thermal energy must be transferred out of 0.510 kg of ethyl alcohol that is initially a gas at 78°C so that it becomes a solid at -114°C?18. Metric-Nonmetric Nonmetric version: How long does a 2.0 x 105 Btu/h water heater take to raise the temperature of 40 gal of water from 70°F to 100°F? Metric version: How long does a 59 kW water heater take to raise the temperature of 150 L of water from 21°C to 38°C?19. Buick A 1500 kg Buick moving at 90 km/h brakes to a stop, at a uniform rate and without skidding, over a distance of 80 m. At what average rate is mechanical energy transformed into thermal energy in the brake system?20. Solar Water Heater In a solar water heater, radiant energy from the Sun is transferred to water that circulates through tubes in a rooftop collector. The solar radiation enters the collector through a transparent cover and warms the water in the tubes; this water is pumped into a holding tank. Assume that the efficiency of the overall system is 20% (that is, 80% of the incident solar energy is lost from the system). What collector area is necessary to raise the temperature of 200 L of water in the tank from 20°C to 40°C in 1.0 h when the intensity of incident sunlight is 700 W/m2?21. Steam What mass of steam at 100°C must be mixed with 150 g of ice at its melting point, in a thermally insulated container, to produce liquid water at 50°C?22. Iced Tea A person makes a quantity of iced tea by mixing 500 g of hot tea (essentially water) with an equal mass of ice at its melting point. If the initial hot tea is at a temperature of (a) 90°C and (b) 70°C, what are the temperature and mass of the remaining ice when the tea and ice reach a common temperature? Neglect energy transfers with the environment.23. Ice Cubes (a) Two 50 g ice cubes are dropped into 200 g of water in a thermally insulated container. If the water is initially at 25°C, and the ice comes directly from a freezer at -15°C, what is the final temperature of the drink when the drink reaches thermal equilibrium? (b) What is the final temperature if only one ice cube is used?24. Thermos of Coffee An insulated Thermos contains 130 cm3 of hot coffee, at a temperature of 80.0°C. You put in a 12.0 g ice cube at its melting point to cool the coffee. By how many degrees has your coffee cooled once the ice has melted? Treat the coffee as though it were pure water and neglect energy transfers with the environment.Sec. 19-8 â–  Some Special Cases of the First Law of Thermodynamics25. Gas Expands A sample of gas expands from 1.0 m3 to 4.0 m3 while its pressure decreases from 40 Pa to 10 Pa. How much work is done by the gas if its pressure changes with volume via each of the three paths shown in the P-V diagram in Fig. 19-30?26. Work Done Consider that 200 J of work is done on a system and 70.0 cal of thermal energy is transferred out of the system. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of (a) W, (b) Q, and (c) A£""?27. Closed Chamber Gas within a closed chamber undergoes the cycle shown in the P-V diagram of Fig. 19-31. Calculate the net thermal energy added to the system during one complete cycle.28. Thermodynamic A thermodynamic system is taken from an initial state A to another state B and back again to A, via state C, as shown by path ABCA in the P-V diagram of Fig. 19-31a. (a) Complete the table in Fig. 19-32b by filling in either + or - for the sign of each thermodynamic quantity associated with each step of the cycle, (b) Calculate the numerical value of the work done by the system for the complete cycle ABCA.29. From i to / When a system is taken from state i to state / along path iaf in Fig. 19-33. Q = 50 cal and W = 20 cal. Along path ibf, Q = 36 cal. (a) What is W along path ibfl (b) If W = -13 cal for the return path fi, what is Q for this path? (c) Take Efl = 10 cal. What is E'fl (d) If Ef' = 22 cal, what are the values of Q for path ib and path bp.30. Gas Within Gas within a chamber passes through the cycle shown in Fig. 19-34. Determine the thermal energy transferred by the system during process CA if the thermal energy added Qab>Sec. 19-9 â–¡ More on Temperature Measurement