What is heat capacity? Paragraph v '. - 23W -_ ' E Path: p Explain why, although similar, one of these statements is false. 1. To raise the temperature, heat must be added. 2. If heat is added, the temperature must rise. 1) 2) 3) 4) 5) Please correct the following sentences. a) This television only uses 200 J of energy! b) Burning a gallon of gasoline releases a lot of power. 0) There is a lot of power stored in the nucleus. (1) It takes a lot more energy to lift the heavy mass quickly than to raise it the same height slowly. e) In the twenty ve years it has been in operation, the power plant has never produced power at a rate faster than yesterday. An adult male needs about 2500 Cal/day to be healthy. How much power is this? What home appliance is about the same rate of energy consumption as an adult human male? A typical car engine might produce about 150 hp. How many typical US homes could this power? Does this surprise you? A typical US home uses about 1.25 kW of power. Imagine you want to generate electricity using geothermal temperature differences. Geothermal heating of rocks and water in the crust can sometimes reach temperatures of as high as 370C. What would be the maximum theoretical efficiency that could be obtained for converting this thermal energy into electricity? Treat the heat engine as if it was a Carnot engine, and assume the conversion of mechanical to electrical energy is 100%. How much energy would be released by fusing two deuterium nuclei to form 3He and release a neutron (d + d > 3He + n)? What if you had 1 kg of deuterium? Note: you can look up masses at htt s://www.nist. ov/ ml/atomicwei ts-and-isoto iccom ositionsrelative-atomic-masses. The mass of the neutron is 1.00866491588 u where u is the unified atomic mass unit, equal to 931.5 MeV/cz. 2 . 87 g of lead at 100 .C was combined with 51 g of water at 22 .C and the final temperature was 26 .C. The heat capacity of lead = 0.0305 cal/g C 3. 87 g of lead at 100 .C was combined with 51 g of ice at 0 .C and the final temperature was 0 .C. Only 3.3 g of ice melted. The latent heat of ice is 80 cal/g. Now, predict what will happen in the following scenarios! Lead at 18 .C is added to 73 g of water at 100 .C. How much lead would you need to add to result in a final temperature of 45 .C? 5. 3.0 g of ice at 0 'C was placed on 23 g of lead at 85 .C. What is the final temperature? How much ice melts? To answer this consider the maximum heat that could be transferred by cooling lead or melting ice.Heat Capacity Calculations Introduction Science is a search for understanding is through generalizations, and the following is a good example. These handful of quantitative relationships can be applied to a multitude of diverse experiments on heat and temperature. They have great explanatory power for experiments we have already done. Furthermore, these relationships are predictive. They enable us to predict the outcome of experiments we haven't done yet! Transfer of heat between objects can be understood in terms of four principles: 1. Conservation of heat. All of the heat lost by an object must be gained by surrounding objects. qlost = qgain 2. Given enough time, objects in contact with each other and insulated from external sources of heat, will all reach thermal equilibrium. Regardless of initial temperature (Ti) they will all end up the same final temperature (TF). If = If 3. The amount of heat (q) given off or absorbed by an object when it changes temperature depends on several things: how large the object is (it's mass, m), what the object is made of (it's constant based on chemical identity, C), and how much the temperature changes (AT). These relationships are summarized in the following equation: q = mCAT 4 . The amount of heat (q) associated with a phase transitions such as melting or vaporization, latent heat, depends on how much of the substance there is (it's mass, m) and what it is made of (it's constant based on chemical identity, H). q = mH Questions Confirm that the above relationships accurately explain the results of the following experiments. By putting numbers into the equations, show that heat gained and lost in each case are equal. 1. 87 g of water at 100 .C was combined with 51 g of water at 22 .C and the final temperature was 71 .C. The heat capacity of water = 1 cal/g C