One mole of ideal gas is slowly compressed to one-third of its original volume. in this compression, the work done on the gas ha
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Answer:
Work: 4.0 kJ, heat: 4.25 kJ
Explanation:
For a gas transformation at constant pressure, the work done by the gas is given by
where in this case we have:
is the pressure
is the initial volume
is the final volume
Substituting,
The 1st law of thermodynamics also states that
where
is the change in internal energy of the gas
Q is the heat absorbed by the gas
Here we know that
Therefore we can re-arrange the equation to find the heat absorbed by the gas:
The momentum p of a moving particle is the product between its mass, m, and tis velocity, v:
In our problem, we know
and 
, and using the relationship mentioned above, we can find the mass m of the particle:
In our problem, we know
Answer:
1.92 x 10⁻¹²J
Explanation:
The magnetic force from the magnetic field gives the circulating protons gives the particle the necessary centripetal acceleration to keep it orbiting round the circular path. And from Newton's second law of motion, the force(F) is equal to the product of the mass(m) of the proton and the centripetal acceleration(a). i.e
F = ma
Where;
a = [v = linear velocity, r = radius of circular path]
=> F = m ------------(i)
We also know that the magnitude of this magnetic force experienced by the moving charge (proton) in a magnetic field is given by;
F = q v B sin θ ----------(ii)
Where;
q = charge of the particle
v = velocity of the particle
B = magnetic field
θ = the angle between the velocity and the magnetic field.
Combining equations (i) and (ii) gives
m = q v B sin θ [θ = 90° since the proton is orbiting at the maximum orbital radius]
=> m = q v B sin 90°
=> m = q v B
Divide both side by v;
=> m = qB
Make v subject of the formula
v =
From the question;
B = 1.25T
m = mass of proton = 1.67 x 10⁻²⁷kg
r = 0.40m
q = charge of a proton = 1.6 x 10⁻¹⁹C
Substitute these values into equation(iii) as follows;
v =
v = 4.79 x 10⁷m/s
Now, the kinetic energy, K, is given by;
K = mv²
m = mass of proton
v = velocity of the proton as calculated above
K =
K = 1.92 x 10⁻¹²J
The kinetic energy is 1.92 x 10⁻¹²J