A swimming pool filled with water has dimensions of 4.76 m ✕ 10.2 m ✕ 1.70 m. Water has density ρ = 1.00 ✕ 103 kg/m3 and specific heat c = 4186 J/(Kg◦°C). Find the mass (in kg) of water in the pool. 2. Find the thermal energy (in J) required to heat the pool water from 3°C to 27.1°C. 3. Calculate the cost (in dollars) of heating the pool from 3°C to 27.1°C if electrical energy costs $0.120per kilowatt-hour.

A swimming pool filled with water has dimensions of 4.76 m ✕ 10.2 m ✕ 1.70 m. Water has density ρ = 1.00 ✕ 103 kg/m3 and specific heat c = 4186 J/(Kg◦°C). Find the mass (in kg) of water in the pool. 2. Find the thermal energy (in J) required to heat the pool water from 3°C to 27.1°C. 3. Calculate the cost (in dollars) of heating the pool from 3°C to 27.1°C if electrical energy costs $0.120per kilowatt-hour.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter21: Heat And The First Law Of Thermodynamics

Section: Chapter Questions

Problem 71PQ

See similar textbooks

Similar questions

A silver kettle weighs 1.07 kg. (The specific heat of silver is 0.235 J/g·°C) (a) What is the heat capacity (in J/°C) of the kettle? _____ J/°C (b) How much heat (in J) is required to increase the temperature of this kettle from 20.5°C to 98.7°C? _____ J (c) How much heat (in J) is required to heat this kettle from 20.5°C to 98.7°C if it contains 1.03 L of water (density of 0.997 g/mL and a specific heat of 4.18 J/g·°C across the temperature range)? _____ J
A swimming pool filled with water has dimensions of 5.01 m ✕ 12.2 m ✕ 1.74 m. Water has density ρ = 1.00 ✕ 103 kg/m3 and specific heat c = 4186 J (kg · °C) . HINT (a) Find the mass (in kg) of water in the pool. ?kg (b) Find the thermal energy (in J) required to heat the pool water from 16.3°C to 26.1°C. ?J (c) Calculate the cost (in dollars) of heating the pool from 16.3°C to 26.1°C if electrical energy costs $0.105 per kilowatt-hour. $ ?
A window has dimensions of 1.6 m by 2.85 m and is made of glass 7.25 mm thick. On a winter day, the outside temperature is 24° C while the inside temperature is a comfortable at 19.5° C. (k of glass =0.195W/m.K) (1.5+1.5+2 = 5marks)Calculate the following:a) the area of the window in square metres Answer for part 1 .b) the temperature gradient (ΔT/Δx)in kelvin/metre Answer for part 2 .c) the rate of heat lost through the window by conduction in watts Answer for part 3 .
A common practice for a person with a high fever is to take a bath in cool water. Assuming an 80 kg person is really ill and needs to cool down from 40°C to 37°C. What is the minimum amount of water needed for bathing assuming the water begins at room temperature, 25°C? The specific heat of the body on average is 3470 J/kg°C and water is 4186 J/kg°C. 16.6 kg 212.2 kg 200 kg 19.8 kg
A copper cylinder has a mass of 0.0758 kg and a specific heat of 386 J/kg Co. It is heated to 80.5° C and then put in 0.0657 kg of unknown liquid whose temperature is 19.5° C. The final temperature of the mixture is 31.9° C. What is the specific heat of the unknown liquid? a. 875 J/kg C b. 1000 J/kg C c. 900 J/kg C d. 1745 J/kg C
What is the cost of heating water in a swimming pool of radius 3.5 m and depth 1.3 m from 13 degress celcius to 27 degress Celcius. If the price of energy is $0.08/ KWh. The specific heat of water is 4186 J/Kg/Cdegrees and density of water is 1000 Kg/m^3. (Hint: Volume of cylinder is πr2h) A. $30.25 B. $65.15 C. $95.50 D. $25.25 E. $133
A 880 cm X 1680 cm house is built on a 15.6 cm thick concrete slab of thermal conductivity 0.62 W/m.K.. If the ground temperature of the slab is 7.6ºC while the interior of the house is 21ºC. Calculate the following: a) The temperature difference in kelvin Answer for part 1 . b) The temperature gradient (ΔT/Δx) in kelvin/metre Answer for part 2 . c) The heat loss rate through the concrete slab in kilowatt Answer for part 3 .
A 56 kW electric furnace measures 1.2m x 1.3m x 0.7m. When the temperature inside the furnace is 1613 ºC, a block of aluminum with a mass of 283 kg and a temperature of 18 ºC is placed inside. Assuming the heat loss from the furnace walls is 529 W/m, how long (in min) will it take to heat the block to the furnace temperature? (Specific heat of aluminum is 0.90 kJ/kg. K)
An engineer who is working on the heat transfer analysis of a house in English units needs the convection heat transfer coefficient on the outer surface of the house. But the only value he can find from his handbooks is 22 W/m2·K, which is in SI units. The engineer does not have a direct conversion factor between the two unit systems for the convection heat transfer coefficient. Using the conversion factors between W and Btu/h, m and ft, and °C and °F, express the given convection heat transfer coefficient in Btu/h·ft2·°F.
A rectangular block of aluminum has the following dimensions: 1m x 1m x m. The density of aluminum is 2700kg/m^3. The specific heat of aluminum is 0.9 J/g K. How much does the block of aluminum weigh in Newtons?
A certain amount of heat is added to a mass of aluminum (c=0.21 cal/g•°C), and its temperature is raised 57°C. Suppose that the same amount of heat is added to the same mass of copper (c=0.093 cal/g•°C). How much does the temperature of the copper rise? Answers: a. 3.2 x 10^2 degree Celsius b. 1.8 x 10^3 degree Celsius c. 1.3 x 10^2 degree Celsius d. 2.3 x 10^2 degree Celsius
A tank of 10ft3 capacity is half filled with glycerin. The weight density of glycerin is 78.6 lbs/ft3 and its specific heat is 0.57 BTU/lb-°F. (a) How much heat is needed to raise the temperature of glycerin from 40°F to 70°F? (b) If the heat supplied to the glycerin is at a rate of 750 BTU/min, at what rate does its temperature rises? (INCLUDE FBD)