Question

Kimonyoski takes a 9-minute shower every day. The shower uses about 1.8 gal per minute of water. He also uses 23 gallons of hot water per day for clothes and dish washers. The hot water heats the water from 60 to 110 F. What is the total energy required per week for hot water

Answer 1

Step-by-step explanation:

watr used for shower = 1.8 gallon per minute

Total water used for shower in 9 minutes , V = 1.8 x 9 = 16.2 gal per day

Water used for washing, V' = 23 gal per day

initial temperature of water, T1 = 60 F = 15.56 °C

final temperature of water, T2 = 110 F = 43.33 °C

Total Volume of water used per day = (23 + 16.2) x 3.785 litre

total mass, m = 148.372 kg

Heat required, H = mass x specific heat of water x rise in temperature

H = 148.372 x 4200 x (43.33 - 15.56)

H = 1.73 x 10^7 Joule

Answer 2

`q=120731598.109\ J=1.2* 10^8\ J`

Step-by-step explanation:

Given:

time of shower usage each day,
`t=9\ min`

flow rate through the shower,
`\dot V_s=1.8\ gal.min^(-1)`

volume of water used for washing each day,
`V_w=23\ gal`

initial temperature of water,
`T_i=60\ F=15.56\ ^(\circ)C`

final temperature of water,
`T_f=110\ f=43.33\ ^(\circ)C`

Now the total volume of water used each day:

`V=\dot V_s* t+V_w`

`V=1.8* 9+23`

`V=39.2\ gal=148.3881\ L`

We know that the mass of 1 L of water is 1 kg, so the mass of water used each day:

`m=148.3881\ kg`

Heat energy required for heating the water each day within the given temperature range:

`Q=m.c.(T_f-T_i)`

where:

c = specific heat capacity of water =
`4184\ J.kg^(-1).K^(-1)`

`Q=148.3881* 4184* (43.33-15.56)`

`Q=17247371.1584\ J`

Now the energy required per week:

`q=Q* 7`

since there are 7 days in a week

`q=17247371.1584* 7`

`q=120731598.109\ J=1.2* 10^8\ J`