Respuesta :
A) Q1 = (3/2)P1V1[A – 1]
B) W2 = P1V1(In A)
C) W3 = P1V1(1 – A)
The only source of energy for a monatomic ideal gas (such as helium, neon, or argon) is translational kinetic energy.
A) first law of thermodynamics we have;
ΔU = Q – W
Where,
ΔU = change in internal energy
Q = the heat absorbed
W = the work done
the first process occurs at constant volume, the work done is zero:
Thus,
ΔU = Q – 0
ΔU = Q
The change in internal energy is;
ΔU = nCvΔt
where;
n = number of moles of the gas
R = gas constant,
Cv = specific heat at constant volume
Δt = change in temperature i.e T2 – T1.
Using the ideal gas law, find an n and Δt
P1V1 = nRT1
n = P1V1/RT1
T1 = P1V1/nR
the specific heat at constant volume is Cv = (3/2)R
From the question, pressure has reached AP1, calculate the temperature T2 by using the ideal gas law;
AP1V1 = nRT2
T2 = AP1 V1/ nR
heat added in terms of p1, V1, and A
Q = ΔU = nCv(T2 – T1)
From earlier
T1 = P1V1/nR
Putting equation of T2 and T1 into the energy equation;
Q = nCv((AP1 V1/ nR) – P1V1/nR)
Q = Cv • P1V1/R (A – 1)
we saw that Cv = (3/2)R. Thus,
Q = (3/2)R • P1V1/R (A – 1)
Q = (3/2)P1V1[A – 1]
B) Here again, work done in step 2 in terms of p1, V1, and A.
The process is an isothermal process because temperature is constant; so work done W = nRT In(V2/V1)
T = T1 (temperature is constant)
From earlier,
n = P1V1/RT1 and
But in this process, it’s
n = P1V1/RT1 and thus,
V2 = nRT2/P1
Also, T2 = AP1 V1/ nR
V1 = nRT2/AP1
Putting the values into, W = nRT In(V2/V1),
W = (P1V1/RT1) • RT1 • In((nRT2/P1)/(nRT2/AP1)
W = P1V1(In A)
C) In step 3,we have and isobaric process because the pressure is constant.
Work done; W = P(V1 – V2)
V2 is the final volume while V1 is the the initial volume
P is P1 (isobaric process).
From earlier, we saw that,
V1 = nRT2/AP1 and V2 = nRT2/P1
And that T2 = AP1 V1/ nR
Thus,
V1 = V1 and V2 = AV1
Thus, W = P1(V1 – AV1) = P1V1(1 – A)
Learn more about the monatomic ideal gas with the help of the given link:
https://brainly.com/question/8893537
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I understand that the question you are looking for is "A monatomic ideal gas has pressure p1 and temperature T1. It is contained in a cylinder of volume V1 with a movable piston, so that it can do work on the outside world. Consider the following three-step transformation of the gas: The gas is heated at constant volume until the pressure reaches Ap1 (where A>1). The gas is then expanded at constant temperature until the pressure returns to p1. The gas is then cooled at constant pressure until the volume has returned to V1.
It may be helpful to sketch this process on the pVplane.
How much heat Q1 is added to the gas during step 1 of the process?
Express the heat added in terms of p1, V1, and A.
How much work W2 is done by the gas during step 2?
Express the work done in terms of p1, V1, and A.
How much work W3 is done by the gas during step 3?
If you've drawn a graph of the process, you won't need to calculate an integral to answer this question.
Express the work done in terms of p1, V1, and A."
