16. A kettle used at a building site is filled with 25 liters of water at 16 ℃. The water is heated until it reaches 90 ℃. Calculate the amount of heat required in kJ. A) 7.74 x 106 kJ C) 7.74 x 103 kJ B) 1.11 x 107 kJ D) 1.11 x 104 kJ
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Answer:
Reservoir
T
0
=1000°C
R
1
=0.25m
Outer radius R
2
=0.50m
Initially filled with water at T=0°C
The thermal conductivity of the material K=
4π
10
2
W/m−K
Heat capacity is negligible
Find the time required to raise the temperature of water to 100°C
Take specific heat of water S=4.2KJ/kg°C
Density of water d=1000kg/m
3
The formula will be
Q
cond.sph
=
R
sph
T
1
−T
2
R
sph
=
4πr
1
r
2
K
r
2
−r
1
R
sph
=
4π×0.50×0.25×10
2
(0.50−0.25)×4π
R
sph
=
0.25×0.50×10
2
0.25
=
50×10×10
100
=
50
1
m
Now,
T
2
=1000+273=1273K
T
1
=273K
Q=
50
1
1273−273
=50000columb
t=
42×1000
50000×10
=121.42s
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