Answer:
2,38kg
Explanation:
Mass in function of time can be found by the formula: , where is the initial mass, t is the time and k is a constant.
Given that a sample decay 1% per day, that means that after first day you have 99% of mass.
, but , so we have , then
Now using k found we must to find .
Middle school? lol but, the third one.
You have effectively got two capacitors in parallel. The effective capacitance is just the sum of the two.
Cequiv = ε₀A/d₁ + ε₀A/d₂ Take these over a common denominator (d₁d₂)
Cequiv = ε₀d₂A + ε₀d₁A / (d₁d₂) Cequiv = ε₀A( (d₁ + d₂) / (d₁d₂) )
B) It's tempting to just wave your arms and say that when d₁ or d₂ tends to zero C -> ∞, so the minimum will occur in the middle, where d₁ = d₂
But I suppose we ought to kick that idea around a bit.
(d₁ + d₂) is effectively a constant. It's the distance between the two outer plates. Call it D.
C = ε₀AD / d₁d₂ We can also say: d₂ = D - d₁ C = ε₀AD / d₁(D - d₁) C = ε₀AD / d₁D - d₁²
Differentiate with respect to d₁
dC/dd₁ = -ε₀AD(D - 2d₁) / (d₁D - d₁²)² {d2C/dd₁² is positive so it will give us a minimum} For max or min equate to zero.
-ε₀AD(D - 2d₁) / (d₁D - d₁²)² = 0 -ε₀AD(D - 2d₁) = 0 ε₀, A, and D are all non-zero, so (D - 2d₁) = 0 d₁ = ½D
In other words when the middle plate is halfway between the two outer plates, (quelle surprise) so that
d₁ = d₂ = ½D so
Cmin = ε₀AD / (½D)² Cmin = 4ε₀A / D Cmin = 4ε₀A / (d₁ + d₂)
Complete question:
(b) How much energy must be supplied to boil 2kg of water? providing that the specific latent heat of vaporization of water is 330 kJ/kg. The initial temperature of the water is 20 ⁰C
Answer:
The energy that must be supplied to boil the given mass of the water is 672,000 J
Explanation:
Given;
mass of water, m = 2 kg
heat of vaporization of water, L = 330 kJ/kg
initial temperature of water, t = 20 ⁰C
specific heat capacity of water, c = 4200 J/kg⁰C
Assuming no mass of the water is lost through vaporization, the energy needed to boil the given water is calculated as;
Q = mc(100 - 20)
Q = 2 x 4200 x (80)
Q = 672,000 J
Q = 672,000 J
Q = 672,000 J
Therefore, the energy that must be supplied to boil the given mass of the water is 672,000 J
First of all, you didn't tell us WHO measured the "10 years".
If it was the people on Earth, then 10 years passed according to them.
If it was 10 years on the space traveler's clock, then the clock in the
OTHER place, like on Earth, is subject to the relativistic 'time dilation'.
If the clocks are moving relative to each other, then the time interval measured
on either clock is equal to the interval measured on the other clock, divided by
√(1 - v²/c²) .
You said that v/c = 0.85 .
v²/c² = (0.85)² = 0.7225
1 - v²/c² = 1 - 0.7225 = 0.2775
√(1 - v²/c²) = √0.2775 = 0.5268
If one clock counts up 10 years, then the other one counts up
(10years) / 0.5268 = <em>18.983 years </em>
I believe that's the way to do this, and I'll gladly take your points,
but let me recommend that you get a second opinion before you
actually take off on your 10-year interstellar mission.