A 6.5 l sample of nitrogen at 25◦c and 1.5 atm is allowed to expand to 13.0 l. the temperature remains constant. what is the fin
1 answer:
Since the temperature of the gas remains constant in the process, we can use Boyle's law, which states that for a gas transformation at constant temperature, the product between the gas pressure and its volume is constant:
which can also be rewritten as
(1)
where the labels 1 and 2 mark the initial and final conditions of the gas.
In our problem,
, 
and 
, so the final pressure of the gas can be found by re-arranging eq.(1):
Therefore the correct answer is
<span>1. 0.75 atm</span>
which can also be rewritten as
where the labels 1 and 2 mark the initial and final conditions of the gas.
In our problem,
Therefore the correct answer is
<span>1. 0.75 atm</span>
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A)
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:
Using (2) we can rewrite this as
And using (1), we find
Substituting into the last equation, we find the value of x:
B)
In this case, the kinetic energy is 1/10 of the total energy:
Since we have
we can write
And so we find: