Title 2. ANSWER TUTORIAL 2 CH14.pdf ✅

Chapter 14: Temperature and Heat By Miss Y @fizikAsper 5. The Andong Dam Lake in South Korea holds 1.25 ×109 m3 of water. a. How much energy is required to raise the temperature of that volume of water from 11.0°C to 12.0°C? b. How many years would it take an 80.0-MW power plant to supply that amount of energy? [5.23 ×1015 J, 2.07 yr] a. 9 12 m V kg = =  =   (1000)(1.25 10 ) 1.25 10 12 15 Q mc T =  = − (1.25 10 )(4186)(12 11  =) 5.23 10  J b. Q P t = 15 6 5.23 10 65375000 80 10 Q t s P  = = =  1min 1 1 1 65375000 60 60mi 2 n 24 365 .07 h day yr s s h day     = yr 6. A swimming pool filled with water has dimensions of 5.00 m × 10.0 m × 1.78 m. a. Find the mass of water in the pool. b. Find the thermal energy required to heat the pool water from 15.5°C to 26.5°C. c. Calculate the cost of heating the pool from 15.5°C to 26.5°C if electrical energy costs $0.100 per kilowatt-hour. [8.90 ×104 kg, 4.10 ×109 J, $114] a. 4 m = =   = V (1000)(5 10 1.78) 8.90 kg b. 9 Q mc T =  = − = (89000)(4186)(26.5 15.5) 4.10 10  J c. 9 1 4.1 10 1138.89 3600 h Pt Q Ws kWh s = =   = $0.10 1138.89 $114 1 kWh kWh  = 7. An aluminum cup contains 225 g of water and a 40 g copper stirrer, all at 27°C. A 400 g sample of silver at an initial temperature of 87°C is placed in the water. The stirrer is used to stir the mixture until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup. [80 g] (900)(32 27) (0.225)(4186)(32 27) (0.04)(387)(32 27) (0.4)(234)(87 3 8 ) .0 0 2 0 8 absorb release Al Al w w cu cu ag ag Al Al Q Q m c T m c T m c T m c T m m kg g =  +  +  =  − + − − = = + − = 8. A Styrofoam cup holds 0.275 kg of water at 25°C. Find the final equilibrium temperature after a 0.10 kg block of copper at 90°C is placed in the water. Neglect any thermal energy transfer with the Styrofoam cup. [27 °C]
Chapter 14: Temperature and Heat By Miss Y @fizikAsper (0.275)(4186)( 25) (0.1)(387)(90 ) 1151.15( 25) 38.7(90 ) 1151.15 28778.75 3483 38.7 1189.85 32261 2 .75 7 absorb release w w cu cu Q Q m c T m c T T T T T T T T T C =  =  − = − − = − − = − = =  9. An unknown substance has a mass of 0.125 kg and an initial temperature of 95°C. The substance is then dropped into a calorimeter made of aluminum containing 0.285 kg of water initially at 25°C. The mass of the aluminum container is 0.15 kg, and the temperature of the calorimeter increases to a final equilibrium temperature of 32°C. Assuming no thermal energy is transferred to the environment, calculate the specific heat of the unknown substance. [1.18 ×103 J/kg °C] (0.15)(900)(32 25) (0.285)(4186)(32 25) (0.125)( )(95 32) 1180.45 / absorb release Al Al w w u u u u Q Q m c J k T m c T c T c g m c C =  +  =  − + − = − = g 10. How much thermal energy is required to boil 2.00 kg of water at 100°C into steam at 125°C? The latent heat of vaporization of water is 2.26 ×106 J/kg and the specific heat of steam is 2010 J/kg°C. [4.62 ×106 J] 6 6 Q mL mc T = + + =  =  − (2)(2.26 10 ) (2)(2010)(125 100) 4 6 1 . 2 0  J 11. Steam at 100°C is added to ice at 0°C. a. Find the amount of ice melted and the final temperature when the mass of steam is 10 g and the mass of ice is 50 g. b. Repeat with steam of mass 1.0 g and ice of mass 50 g. [50 g, 40°C, 8 g, 0°C] a. 5 6 (0.05)(3.33 10 ) (0.05)(4186)( 0) (0.01)(2.26 10 ) (0.01)(4186)(100 ) 16650 40.3 209.3( ) 226 6 00 41.86(100 ) absorb release ice ice w steam steam w Q Q m L m c T m L m c T T T T T T C = +  = +   + − =  + − + = + − =  b. 5 6 5 (3.33 10 ) (0.001)(2.26 10 ) (0.001)(4186)(100 0) (3. 0.008 8 33 10 ) 2260 418.6 absorb release ice steam steam w ice ice ice Q Q m L m L m c T m k g m m g = = +   =  + −  = + = =