Heat and Temperature Change Physics news Definitions Heat and Temperature Change Examples Heat and Phase Change Mechanisms of Heat Flow Conduction Convection Radiation

Off-Topic: Physics News Discovery of Gravitational Waves (2016 Feb 11) http://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html https://www.washingtonpost.com/news/speaking-of-science/wp/2016/02/11/cosmic-breakthrough-physicists-detect-gravitational-waves-from-violent-black-hole-merger http://www.wsj.com/articles/gravity-waves-detected-vindicating-einstein-1455207960 http://www.bbc.com/news/science-environment-35524440 Einstein’s General Theory of Relativity Gravity bends space and time. Proven correct for 100 years Also predicts gravitational waves (confirmed yesterday)

Off-Topic: Physics News LIGO detector Splits laser beam, travel 2 different paths, recombine Recombination causes interference pattern (Giancoli 12-6) Gravity wave passing through both paths change interference pattern 2 detectors, one in Louisiana, one in Washington state

Off-Topic: Physics News Results Collision of 2 Black holes Signal detected simultaneously in WA and LA https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102

Heat - Definition Energy Transfer by non-mechanical means Heating water on stove (chemical/electrical) Burning gasoline in engine (chemical) Touching a hot/cold object (conduction) Losing heat through glass window (conduction) Feeling heat from sun (electromagnetic) Heating food in microwave (electromagnetic) Each involves energy transfer by non-mechanical means and raising/lowering of temperature Heat flows from “hot” to “cold”

Heat - Definitions Units of Heat. Calorie (food) Mechanical Equivalent Calorie - heat required to raise 1 g water 1°C Kilocalorie - 1000 calories Calorie (food) Actually uses kilocalories Heat given off by incinerating Mechanical Equivalent 1 cal = 4.186 J 1 kcal = 4.186 kJ Mechanical equivalent – Friction - > Heat Electrical equivalent – Electrical Energy - > Heat

Heat and Internal Energy Total thermal energy contained. 𝑈=𝑁 1 2 𝑚 𝑣 2 = 3 2 𝑁𝑘𝑇= 3 2 𝑛𝑅𝑇 Heat Non-mechanical input or output ∆𝑈=𝑄 U Q

Heat and Temperature Change Adding heat to object causes temperature change. 𝑄=𝑚𝑐∆𝑇 Q – Quantity of Heat (J) (cal) m – Mass (kg) c – Specific Heat ( J/kg C°) ΔT – Temperature change (C°)

Specific Heat and Temperature Change Specific Heat measures ability to absorb heat and distribute to molecules. 𝑄=𝑚𝑐∆𝑇 Table 14-1 Water, wood, etc Why is water a coolant?

Example 14-2 Empty 𝑄=𝑚𝑐∆𝑇=(20 𝑘𝑔)(450 𝐽 𝑘𝑔 𝐶°) 80 𝐶° =720 𝑘𝐽 (a) How much heat is required to raise the temperature of an empty 20 kg vat made of iron from 10°C to 90°C? (b) What if the vat is filled with 20 kg water? Empty 𝑄=𝑚𝑐∆𝑇=(20 𝑘𝑔)(450 𝐽 𝑘𝑔 𝐶°) 80 𝐶° =720 𝑘𝐽 Filled with 20 kg water 𝑄=𝑚𝑐∆𝑇=(20 𝑘𝑔)(450 𝐽 𝑘𝑔 𝐶°) 80 𝐶° + (20 𝑘𝑔)(4186 𝐽 𝑘𝑔 𝐶°) 80 𝐶° =720 𝑘𝐽+6698 𝑘𝐽=7418 𝑘𝐽

Example 14-3 – Hot pan in the sink - 1 5 kg skillet at 200°C placed in sink with 40x50x10 cm water at 20°C. What is final temperature? Mass of water 40 𝑐𝑚∙50 𝑐𝑚 ∙10 𝑐𝑚=20,000 𝑐𝑚 3 =20 𝐿=20 𝑘𝑔 Requirement for equilibrium Heat lost by skillet = heat gained by water. Final temperature same. Heat exchange equation: 𝑚 𝑠𝑘𝑖𝑙𝑙𝑒𝑡 𝑐 𝑠𝑘𝑖𝑙𝑙𝑒𝑡 ∆ 𝑇 𝑠𝑘𝑖𝑙𝑙𝑒𝑡 = 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 Now just solve..

Example 14-3 – Hot pan in the sink - 2 5 kg skillet at 200°C placed in sink with 20 kg water at 20°C. What is final temperature? Heat exchange equation 𝑚 𝑠𝑘𝑖𝑙𝑙𝑒𝑡 𝑐 𝑠𝑘𝑖𝑙𝑙𝑒𝑡 ∆ 𝑇 𝑠𝑘𝑖𝑙𝑙𝑒𝑡 = 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 Fill in (make each temperature change positive) 5 𝑘𝑔 (450 𝐽 𝑘𝑔 𝐶°) 200 𝐶°− 𝑇 𝑓 = 20 𝑘𝑔 (4186 𝐽 𝑘𝑔 𝐶°) 𝑇 𝑓 −20 𝐶° 450 𝑘𝐽− 2.25 𝑘𝐽 𝐶 𝑇 𝑓 = 83.7 𝑘𝐽 𝐶 𝑇 𝑓 −1674.4 𝑘𝐽 2124.4 𝑘𝐽=(86.0 𝑘𝐽 𝐶 ) 𝑇 𝑓 𝑇 𝑓 =24.7°𝐶 Pan cools more than water heats!

Example 14-4 – Cup cools tea. Heat exchange equation: Heat lost by tea = heat gained by cup. 𝑚 𝑡𝑒𝑎 𝑐 𝑡𝑒𝑎 ∆ 𝑇 𝑡𝑒𝑎 = 𝑚 𝑐𝑢𝑝 𝑐 𝑐𝑢𝑝 ∆ 𝑇 𝑐𝑢𝑝 Fill in (make temperature changes positive) 0. 2 𝑘𝑔 (4186 𝐽 𝑘𝑔 𝐶°) 95 𝐶°− 𝑇 𝑓 = 0.15 𝑘𝑔 (840 𝐽 𝑘𝑔 𝐶°) 𝑇 𝑓 −25 𝐶° 79,500 𝐽− 837 𝐽 𝐶 𝑇 𝑓 = 126 𝐽 𝐶 𝑇 𝑓 −3150 𝐽 82,650 𝐽=(963 𝐽 𝐶 ) 𝑇 𝑓 𝑇 𝑓 =85.8°𝐶 Again the water (tea) dominates

Example 14-5 – 1 hot, 2 cold Wanted to know specific heat of alloy. 0.150 kg sample heated to 540°C, transferred to 400 g water contained in 200 g aluminum calorimeter cup, all at 10.0°C. Finally temperature observed at 30.5°C. 𝑄 𝑙𝑜𝑠𝑡 𝑎𝑙𝑙𝑜𝑦 = 𝑄 𝑔𝑎𝑖𝑛𝑒𝑑 𝑤𝑎𝑡𝑒𝑟 + 𝑄 𝑔𝑎𝑖𝑛𝑒𝑑 𝑐𝑎𝑙𝑜𝑟𝑖𝑚𝑒𝑡𝑒𝑟 Heat exchange equation: (assume water and cup same ΔT) 𝑚 𝑎𝑙𝑙𝑜𝑦 𝑐 𝑎𝑙𝑙𝑜𝑦 ∆ 𝑇 𝑎𝑙𝑙𝑜𝑦 = 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 + 𝑚 𝑐𝑢𝑝 𝑐 𝑐𝑢𝑝 ∆ 𝑇 𝑐𝑢𝑝 0.15 𝑘𝑔 𝑐 𝑎𝑙𝑙𝑜𝑦 509.5°𝐶 = 0.4 𝑘𝑔 (4186 𝐽 𝑘𝑔 𝐶°) 20.5 𝐶° + 0.2 𝑘𝑔 (900 𝐽 𝑘𝑔 𝐶°) 20.5 𝐶° (76.425 𝑘𝑔 𝐶°) 𝑐 𝑎𝑙𝑙𝑜𝑦 =34325 𝐽+3690 𝐽 𝑐 𝑎𝑙𝑙𝑜𝑦 =450 𝐽 𝑘𝑔 𝐶

Problem 11 – cold thermometer in hot water Heat exchange equation: Heat lost by water = heat gained by thermometer 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 = 𝑚 𝑔𝑙𝑎𝑠𝑠 𝑐 𝑔𝑙𝑎𝑠𝑠 ∆ 𝑇 𝑔𝑙𝑎𝑠𝑠 Fill in numbers: 0.135 𝑘𝑔 4186 𝐽 𝑘𝑔 𝐶 𝑇 ℎ −39.2 𝐶 = 0.035 𝑘𝑔 840 𝐽 𝑘𝑔 𝐶 17.6 𝐶 565.1 𝐽 𝐶 𝑇 ℎ −22,152 𝐽=517.44 𝐽 565.1 𝐽 𝐶 𝑇 ℎ =22,669 𝐽 𝑇 ℎ =40.1 𝐶

Problem 12 – hot copper in water + cup Heat exchange equation: (assume water and cup same ΔT) Heat lost by copper = heat gained by water + heat gained by cup 𝑚 𝑐𝑢 𝑐 𝑐𝑢 ∆ 𝑇 𝑐𝑢 = 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 + 𝑚 𝑎𝑙 𝑐 𝑎𝑙 ∆ 𝑇 𝑎𝑙 Fill in numbers: 0.245 𝑘𝑔 390 𝐽 𝑘𝑔 𝐶 285 𝐶− 𝑇 𝑓 = 0.825 𝑘𝑔 4186 𝐽 𝑘𝑔 𝐶 𝑇 𝑓 −12 𝐶 + 0.145 𝑘𝑔 900 𝐽 𝑘𝑔 𝐶 𝑇 𝑓 −12 𝐶 27,231 𝐽− 95.55 𝐽 𝐶 𝑇 ℎ = 3453 𝐽 𝐶 𝑇 ℎ −41,441 𝐽 + 130.5 𝐽 𝐶 𝑇 ℎ −1566 𝐽 70,239 𝐽= 3548 𝐽 𝐶 𝑇 ℎ 𝑇 ℎ =19.8 𝐶

Problem 13 - hot iron in water + vat Heat exchange equation: (assume water and vat same ΔT) Heat lost by horseshoe = heat gained by water + heat gained by vat 𝑚 Ω 𝑐 Ω ∆ 𝑇 Ω = 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 + 𝑚 𝑣𝑎𝑡 𝑐 𝑣𝑎𝑡 ∆ 𝑇 𝑣𝑎𝑡 Fill in numbers: 0.40 𝑘𝑔 450 𝐽 𝑘𝑔 𝐶 𝑇 ℎ −25 𝐶 = 1.35 𝑘𝑔 4186 𝐽 𝑘𝑔 𝐶 5 𝐶 + 0.30 𝑘𝑔 450 𝐽 𝑘𝑔 𝐶 5 𝐶 180 𝐽 𝐶 𝑇 ℎ −4500 𝐽=28,255 𝐽+675 𝐽 180 𝐽 𝐶 𝑇 ℎ =33,430 𝑇 ℎ =185.7 𝐶

Problem 15 How long to supply 318,642 J at 750 J/s (watts) Heat required to heat both coffee and pot 𝑄= 𝑚 𝑤𝑎𝑡𝑒𝑟 𝑐 𝑤𝑎𝑡𝑒𝑟 ∆ 𝑇 𝑤𝑎𝑡𝑒𝑟 + 𝑚 𝑎𝑙 𝑐 𝑎𝑙 ∆ 𝑇 𝑎𝑙 = 0.75 𝑘𝑔 4186 𝐽 𝑘𝑔 𝐶 92 𝐶 + 0.360 𝑘𝑔 900 𝐽 𝑘𝑔 𝐶 92 𝐶 =288,834 𝐽+29,808 𝐽 =318,642 𝐽 How long to supply 318,642 J at 750 J/s (watts) 𝑝𝑜𝑤𝑒𝑟 ∙𝑡𝑖𝑚𝑒=𝑒𝑛𝑒𝑟𝑔𝑦 750 𝐽 𝑠 𝑡=318,742 𝐽 𝑡=425 𝑠 𝑜𝑟 𝑎𝑏𝑜𝑢𝑡 7 𝑚𝑖𝑛𝑢𝑡𝑒𝑠