University of Cebu-METC Alumnos, Mambaling, Cebu City, 6000 2nd Semester School Year 2020-2021 AS101 (Thermodynamics 1) – Energy, Work and Heat Midterm – Exercise No.1 - Solution 1. Air is compressed in a cylinder such that the volume changes from 120 to 20 ππ3 . The initial pressure is 60 psia and the temperature is held constant at 100β. Calculate the work. Solution: π£2 π£2 π = π1 π1 ∫ π ππ = ∫ 2 2 ππ π£2 = π1 π1 πΌπ π π£2 ππ ππ2 ππ‘ 3 20 = (60 2 ) (144 2 ) (120 ππ3 ) ( = −ππππ ππ − πππ ) πΌπ 3 ππ ππ‘ 1728 ππ 120 2. A 40 m x 20 m swimming pool is filled with water to a depth of 2.8 m. Determine the heat required to raise the temperature of the water in the pool from 12β to 29β. Solution: π = π΄πππ π₯ π·πππ‘β = (40 π)(20 π)(2.8 π) π = 2240 π3 π = ππ = (1000 ππ ) (2240 π3 ) = 2.240 π₯ 106 ππ π3 ππ½ ) π₯(29β − 12β) ππ − πΎ πΈ = πππ. ππ π πππ ππ± π = πππ βπ = (2.240 π₯ 106 ππ) (4.18 3. A car engine with a power output of 85 hp has a thermal efficiency of 26 percent. Find the fuel consumption rate of this car if the fuel has a heating value of 20,400 Btu/πππ Solution: ππ‘β = π ππ΄ 0.26 = 85 ππ΄ ππ΄ = 326.923 βπ π₯ π΅π‘π’ βπ 1 βπ 2545 ππ΄ = 832,019.2 π΅π‘π’/βπ ππ΄ = ππ π₯ (π»π»π) π΅π‘π’ π΅π‘π’ 832,019.2 = ππ (20 400 ) βπ πππ πππ ππ = ππ. ππ ππ 4. Water is heated in an insulated, constant diameter tube by a 18-kw electric resistance heater. If the water enters steadily at 20 β and leaves at 100 β, find the mass flow rate of water. Solution: π = πππ βπ ππ½ ππ½ 18 = π (4.18 ) (100 β − 20 β) π ππ − πΆ π = π. πππ ππ/π 5. A freshwater lake with an area of 2400 π2 and an average depth of 5 m is located in a mountainous region which is 350 m above a valley floor. What is the potential energy stored in this lake of water? Solution: πππ π = π΄πππ π₯ ππππ‘β π₯ π·πππ ππ‘π¦ ππ π€ππ‘ππ ππ π = (2400 π2 )(5 π) (1000 3 ) π π = 12 π₯ 106 ππ ππΈ = πππ§ = (12 π₯ 106 ππ) (9.81 π ) (350 π) π 2 π·π¬ = π. ππππ π ππππ π± = πππππ π΄π±
