80.5 J of heat are added to 0.222 moles of a diatomic gas. It expands, doing work, and the temperature goes up by 12.0 K. How mu
1 answer:
The work done by the gas is 25.1 J
Explanation:
The change in internal energy of a diatomic gas is given by the equation
where:
n is the number of moles
R is the gas constant
is the change in temperature
For the gas in this problem:
n = 0.222 mol
Substituting,
Now we can find the work done by the gas using the 1st law of thermodynamics:
where:
Q = +80.5 J is the heat added to the gas
is the change in internal energy
W is the work done by the gas
And solving for W,
And since it is positive, it means that the work is done BY the gas.
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Answer: see the graph attached (straight line, passing through the origin and positive slope).
Justification:
1) Kinetic energy and temperature are in direct proportion. That means:
i) Being kinetic energy y and temperature x: y α x
ii) That implies: y = kx,where k is the constant of proportionality.
iii) The graph is a line that passes through the origin and has positive slope k (k = y / x).
2) The proportional relationship between kinetic energy (KE) and temperature (T) is shown by the Boltzman law, which states:
Average KE = [3 / 2] KT, where K is Boltzman's constant, whose graph is of the form shown in the figure attached.
Justification:
1) Kinetic energy and temperature are in direct proportion. That means:
i) Being kinetic energy y and temperature x: y α x
ii) That implies: y = kx,where k is the constant of proportionality.
iii) The graph is a line that passes through the origin and has positive slope k (k = y / x).
2) The proportional relationship between kinetic energy (KE) and temperature (T) is shown by the Boltzman law, which states:
Average KE = [3 / 2] KT, where K is Boltzman's constant, whose graph is of the form shown in the figure attached.
Answer:
A. when the mass has a speed of zero
Explanation:
In mass-spring system, the velocity and the acceleration are in anti-phase, which means that when one of the two quantities is maximum, the other one is zero, and vice-versa.
In fact:
- When the displacement of the spring is zero (x=0), the velocity is maximum, due to conservation of energy. In fact, as the displacement is zero, the elastic potential energy of the system (given by ) is zero, therefore the kinetic energy (given by
) must be maximum, and so the velocity (v) is also maximum. On the cotnrary, acceleration (a) is directly proportional to the restoring force of the spring, given by
so we see that when x=0, then the force is zero: F=0, and so the acceleration is zero as well.
- When the displacement of the spring is maximum, the velocity is zero, due to conservation of energy. In fact, as the displacement is maximum, the elastic potential energy of the system (given by ) is maximum, therefore the kinetic energy (given by
) must be zero, and so the velocity (v) is also zero. On the cotnrary, since acceleration (a) is directly proportional to the restoring force of the spring, given by
so we see that when x=maximum, then the force is maximum, and so the acceleration is maximum as well.
Based on this, the correct answer is
A. when the mass has a speed of zero