1. A hot tub is filled with 570 gal of watera. What is the volume of water, in liters, in the tub?b. What is the mass, in kilograms, of water in the tub?c. How many kilocalories are needed to heat the water from 62 °F to 105 °F?d. If the hot-tub heater provides 5900 kJ/min, how long, in minutes, will it take to heat the water in the hot tub from 62 °F to 105 °F?

Question
Asked Oct 1, 2019
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1. A hot tub is filled with 570 gal of water

a. What is the volume of water, in liters, in the tub?

b. What is the mass, in kilograms, of water in the tub?

c. How many kilocalories are needed to heat the water from 62 °F to 105 °F?

d. If the hot-tub heater provides 5900 kJ/min, how long, in minutes, will it take to heat the water in the hot tub from 62 °F to 105 °F?

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Expert Answer

Step 1

(a)Volume of water (in Liters) is calculated as follows,

1 gal 3.785 L
Volume of water= 570 gal
= 570 galx3.785 L -2157.45 L
1 gal
Hence, volume of water is 2157.45 L
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1 gal 3.785 L Volume of water= 570 gal = 570 galx3.785 L -2157.45 L 1 gal Hence, volume of water is 2157.45 L

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Step 2

(b) Mass of water (in kg) in the tub is determined as follows,

Density of water=1 kg/L
Mass Density Volume
= (1 kg/L)(2157.45 L) 2157.45 kg
Hence, mass of water in the tub is 2157.45 kg.
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Density of water=1 kg/L Mass Density Volume = (1 kg/L)(2157.45 L) 2157.45 kg Hence, mass of water in the tub is 2157.45 kg.

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Step 3

(c) Heat needed to change the temperature o...

°F (°F -32):
:°C
62°F 16.67 °C
105°F 40.56 °C
Change in temperature, AT = (40.56 °C)-(16.67 °C) = 23.89°C
Heat capacity of water, c
4.18 kJ/ kg°C
Heat needed, q = mcAT
(2157.45 kg) (4.18 kJ/kg°C)(23.89°C) = 2.15x10
kJ
Hence, 2.15 x105 kJ of heat is needed to raise the temperature of water
help_outline

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°F (°F -32): :°C 62°F 16.67 °C 105°F 40.56 °C Change in temperature, AT = (40.56 °C)-(16.67 °C) = 23.89°C Heat capacity of water, c 4.18 kJ/ kg°C Heat needed, q = mcAT (2157.45 kg) (4.18 kJ/kg°C)(23.89°C) = 2.15x10 kJ Hence, 2.15 x105 kJ of heat is needed to raise the temperature of water

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