A mass of 25.5 g of H2O(g) at 373 K is mixed with 325 g of H2O(l) at 285 K and 1 atm. Calculate the final temperature of the sys
1 answer:
Answer:
331.28 K
Explanation:
To solve this problem, you need to know that the heat that the water at 373 K is equal to the heat that the water at 285 K gains.
First, we will asume that at the end of this process there won't be any water left in gaseous state.
The heat that the steam (H20(g)) loses is equal to the heat lost because the change of phase plus the heat lost because of the decrease in temperature:
The specific Heat c of water at 298K is 4.18 kJ/K*kg.
The latent heat cl of water is equal to 2257 kJ/kg.
The heat that the cold water gains is equal to heat necessary to increase its temperature to its final value:
Remember that in equilibrium, the final temperature of both bodies of water will be equal.
Then:
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Answer:
32s
Explanation:
We must establish that by the time the police car catches up to the speeder, both have travelled a certain distance during the same amount of time. However, the police car experiences accelerated motion whereas the speeder travels at a constant velocity. Therefore we will establish two formulas for distance starting with the speeder's distance:
and the police car distance:
Since they both travel the same distance x, we can equal both formulas and solve for t:
Two solutions exist to the equation; the first one being
The second solution will be:
This result allows us to confirm that the police car will take 32s to catch up to the speeder
Answer:
A) = 1.44 kg m², B) moment of inertia must increase
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is
I = ½ m R²
A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is
I = + m D²
Let's apply these equations to our case
The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms
=
+ 2
= ½ M R²
The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body
M = 7/8 m total
M = 7/8 64
M = 56 kg
The mass of the arms is
m’= 1/8 m total
m’= 1/8 64
m’= 8 kg
As it has two arms the mass of each arm is half
m = ½ m ’
m = 4 kg
The arms are very thin, we will approximate them as a particle
= M D²
Let's write the equation
= ½ M R² + 2 (m D²)
Let's calculate
= ½ 56 0.20² + 2 4 0.20²
= 1.12 + 0.32
= 1.44 kg m²
b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase