Suppose that 4.7 moles of a monatomic ideal gas (atomic mass = 8.5 × 10^-27 kg) are heated from 300K to 500K at a constant volume of 0.47 m^3. It may help you to recall that CVCV = 12.47 J/K/mole and CPCP = 20.79 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 10^23) times the number of moles of the gas.

1) How much energy is transferred by heating during this process?
2) How much work is done by the gas during this process?
3) What is the pressure of the gas once the final temperature has been reached?
4) What is the average speed of a gas molecule after the final temperature has been reached?
5) The same gas is now returned to its original temperature using a process that maintains a constant pressure. How much energy is transferred by heating during the constant-pressure process?
6) How much work was done on or by the gas during the constant-pressure process?

1) Q = nc*change T (c = 12.47)

2) No vol change, no work
3)P1/T1 = P2/T2
4) Use 3/2kT = 1/2mv^2
5) Q = nc*change T (c = 20.79)
6) Find new volume, W =P*changeV

To solve the given questions, we can use the following formulas:

1) The energy transferred by heating, Q, can be calculated using the formula:

Q = n * Cv * ΔT
where n is the number of moles, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature.

2) The work done by the gas, W, can be calculated using the formula:

W = 0 (since the volume is constant)

3) The pressure of the gas, P, can be calculated using the ideal gas law:

PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

4) The average speed of a gas molecule, v, can be calculated using the formula:

v = sqrt((3 * kB * T) / m)
where v is the average speed, kB is the Boltzmann constant, T is the temperature, and m is the mass of the gas molecule.

5) The energy transferred by heating during the constant-pressure process can be calculated using the formula:

Q = n * Cp * ΔT
where n is the number of moles, Cp is the molar heat capacity at constant pressure, and ΔT is the change in temperature.

6) The work done on or by the gas during the constant-pressure process can be calculated using the formula:

W = -P * ΔV
where W is the work done, P is the pressure, and ΔV is the change in volume.

Now let's calculate the answers step-by-step:

1) How much energy is transferred by heating during this process?

n = 4.7 moles
Cv = 12.47 J/K/mole
ΔT = 500 K - 300 K = 200 K

Using the formula Q = n * Cv * ΔT:
Q = 4.7 * 12.47 * 200
Q = 1171.58 J

Therefore, the energy transferred by heating during this process is 1171.58 J.

2) How much work is done by the gas during this process?

Since the volume is constant, no work is done by the gas (W = 0).

3) What is the pressure of the gas once the final temperature has been reached?

n = 4.7 moles
R = 8.314 J/(mol * K)
T = 500 K
V = 0.47 m^3

Using the ideal gas law PV = nRT:
P * V = n * R * T
P = (n * R * T) / V

P = (4.7 * 8.314 * 500) / 0.47
P = 5.003 * 10^4 Pa

Therefore, the pressure of the gas once the final temperature has been reached is 5.003 * 10^4 Pa.

4) What is the average speed of a gas molecule after the final temperature has been reached?

m = 8.5 * 10^-27 kg
kB = 1.3806 * 10^-23 J/K
T = 500 K

Using the formula v = sqrt((3 * kB * T) / m):
v = sqrt((3 * 1.3806 * 10^-23 * 500) / (8.5 * 10^-27))
v = 1394.7 m/s

Therefore, the average speed of a gas molecule after the final temperature has been reached is 1394.7 m/s.

5) How much energy is transferred by heating during the constant-pressure process?

n = 4.7 moles
Cp = 20.79 J/K/mole
ΔT = 300 K - 500 K = -200 K

Using the formula Q = n * Cp * ΔT:
Q = 4.7 * 20.79 * (-200)
Q = -1961.64 J

Therefore, the energy transferred by heating during the constant-pressure process is -1961.64 J.

6) How much work was done on or by the gas during the constant-pressure process?

W = -P * ΔV

Since the process maintains a constant pressure, the work done on or by the gas can be calculated using the formula W = -P * ΔV.

However, the change in volume (ΔV) is not provided, so it is not possible to calculate the exact value of work done during the constant-pressure process without this information.

To find the answer to each of these questions, we can use the principles of thermodynamics. Here's how to approach each question:

1) To calculate the energy transferred by heating, we need to use the equation ΔQ = nCΔT, where ΔQ is the heat transferred, n is the number of moles of the gas, C is the molar heat capacity of the gas, and ΔT is the change in temperature.

We're given the number of moles (4.7 moles), the molar heat capacity at constant volume (CVCV = 12.47 J/K/mole) and the change in temperature (ΔT = 500K - 300K = 200K). Using these values, we can plug them into the equation:

ΔQ = (4.7 mol) × (12.47 J/K/mol) × (200 K) = [calculate to get the result]

2) To calculate the work done by the gas, we use the equation ΔW = -PΔV, where ΔW is the work done, P is the pressure, and ΔV is the change in volume.

In this case, the volume remains constant (0.47 m^3), so ΔV = 0. The work done is then ΔW = 0.

3) The pressure of the gas once the final temperature is reached can be found using the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the temperature.

We're given the number of molecules (6.022 × 10^23 molecules/mol × 4.7 mol = [calculate to get the result]) and the volume (0.47 m^3) and the final temperature (500K).

4) The average speed of a gas molecule can be calculated using the equation v = sqrt(3RT / M), where v is the average speed, R is the gas constant, T is the temperature, and M is the molar mass.

We're given the temperature (500K) and molar mass (8.5 × 10^-27 kg). Plugging these values into the equation gives us the average speed.

5) To find the energy transferred by heating during the constant-pressure process, we again use the equation ΔQ = nCΔT, but this time we use the molar heat capacity at constant pressure (CPCP = 20.79 J/K/mole).

We're given the same number of moles (4.7 mol) and the same temperature change (ΔT = 200K), but the molar heat capacity is different. Plug these values into the equation to find the energy transferred.

6) Since the process is done at constant pressure, the work done is given by ΔW = -PΔV. However, since the volume remains constant, ΔW = 0. Thus, no work is done on or by the gas during this constant-pressure process.

Remember to substitute the given values and perform the necessary calculations to find the answers to each of these questions.

For 2 and 5, draw a PV diagram.

2) Isochoric process so we have a vertical line
5) Isobaric process so we have a horizontal line