Suppose you have a gas under 2 atm of pressure and taking up 0.5m ^ 3 of volume. If you compress the gas so that it takes up 0.1
1 answer:
Answer:
10 atm
Explanation:
Assuming the gas is kept at constant temperature, we can apply the following law (Boyle's law):
"For a gas kept at a constant temperature, the pressure of the gas is inversely proportional to its volume"
Mathematically,
where p is the pressure of the gas and V its volume.
The equation can also be rewritten as
Where for the gas in the problem, we have:
is the initial pressure
is the initial volume
is the final pressure
is the final volume
Solving for p2,
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a) Constant
b) Constant
Explanation:
a)
We can answer this question by using the equivalent of Newton's second law of motion of rotational motion, which can be written as:
(1)
where
is the net torque acting on the object in rotation
I is the moment of inertia of the object
is the angular acceleration
The angular acceleration is the rate of change of the angular velocity, so it can be written as
where
is the change in angular velocity
is the time interval
So we can rewrite eq.(1) as
In this problem, we are told that at a given instant, the object has an angular acceleration due to the presence of torques, so there is a non-zero change in angular velocity.
Then, additional torques are applied, so that the net torque suddenly equal to zero, so:
From the previous equation, this implies that
Which means that the angular velocity at that instant does not change anymore.
b)
In this second case instead, all the torques are suddenly removed.
This also means that the net torque becomes zero as well:
Therefore, this means that
So also in this case, there is no change in angular velocity: this means that the angular velocity of the object will remain constant.
So cases (a) and (b) are basically the same situation, as the net torque is zero in both cases, so the object acts in the same way.