Answer:
The minimum heat required is 171626 joules.
Explanation:
By First Law of Thermodynamics, the amount of heat (
), in joules, is equal to the change in internal energy of water. The minimum heat required is the sensible heat necessary to heat up the water. That is:
(1)
Where:
- Density of water, in kilograms per cubic meter.
- Volume of water, in cubic meters.
- Specific heat of water, in joules per kilogram-degree Celsius.
- Change in temperature, in degrees Celsius.
If we know that 
, 
, 
and 
, then the minimum heat required is:
The minimum heat required is 171626 joules.
A halogen atom gives off lots of energy.
Part (a)
Let h = depth of water surface from the top of the well, m
Because the stone is dropped, its initial velocity is zero.
Let t₁ = time for the stone to drop, s
Then
h = (1/2)*(9.8 m/s²)*(t₁ s)²
t₁ = √(h/4.9) s = 0.4518√h s
The velocity of sound is 336 m/s.
The time for the sound wave to travel from the water surface to the top of the well is
t₂ = h/336 m/s
Because the time before the sound is heard is 2.4 s, therefore
t₁ + t₂ = 2.4
0.45181√h + h/336 = 2.4
Multiply through by 336.
151.8082√h + h = 806.4
h - 806.4 = -151.8082√h
h² - 1612.8h + 6.5028 x 10⁵ = 2.3046 x 10⁴h
h² - 2.4659 x 10⁴h + 6.5028 x 10⁵ = 0
Solve with the quadratic formula.
h = 0.5[2.4659 x 10⁴ +/- 2.4606 x 10⁴]
= 24632 m or 26.5 m
Test the two answers.
When h = 24632,
t₁ = 0.4518√(24632) = 70.9 s (Not acceptable)
When h = 26.5 m,
t₁ = 0.4518√(26.5) = 2.3258 s, t₂ = 26.5/336 = 0.0789 s,
t₁+t₂ = 2.4 s (CORRECT)
Answer: h = 26.5 m
Part (b)
If travel time for the sound is ignored, then
0.4518√h = 2.4
h = (2.4/0.45118)² = 28.2 m
The percent error is 100*[(28.2 - 26.5)/26.5] = 6.42%
Answer: The error is 6.4%
Convection can best be observed as she blows the warm steam air that rises.
As the warm steam rises, she forces displaces it with cool air from her mouth. Because the warm steam is less dense it rises and because the cool air is more dense, it displaces the warm air.
This scenario is an example of convection.
Metric unit of lenght is meter (m.)
