A Cylinder is filled with 1.20 mol of He(g) at 25 C under ambient pressure of 0.966 atm. The gas in the cylinder is then heated with 1.430 KJ of heat, and the piston is raised by the expanding gas under the constant ambient pressure. Calculate the following after expansion.

a. final temperature or gas
b. work done by the gas
c. change in internal energy of the gas
d. final volume of gas

To find the final temperature of the gas, we can use the Ideal Gas Law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin

First, let's convert the temperature from Celsius to Kelvin:
T = 25°C + 273.15 = 298.15 K

Next, rearrange the equation to solve for T:
T = PV / nR

Given values:
P = 0.966 atm
V = unknown
n = 1.20 mol
R = 0.0821 atm L / (mol K) (ideal gas constant)

Substituting the values into the equation:
T = (0.966 atm) * V / (1.20 mol * 0.0821 atm L / (mol K))

Now, let's solve for the final temperature:

a. Final Temperature:
T = (0.966 atm) * V / (1.20 mol * 0.0821 atm L / (mol K))
298.15 K = (0.966 atm) * V / (1.20 mol * 0.0821 atm L / (mol K))

To find the work done by the gas, we can use the equation:

Work = -PΔV

Where:
P = pressure
ΔV = change in volume

In this case, the pressure is constant, and we are given the change in volume, which is the amount the piston is raised. Therefore, the work done by the gas is:

b. Work Done:
Work = - P * ΔV
Work = - (0.966 atm) * (unknown)

To find the change in internal energy of the gas, we can use the equation:

ΔU = q - w

Where:
ΔU = change in internal energy
q = heat added to the gas
w = work done by the gas

In this case, we are given the heat added to the gas, and we can calculate the work done by the gas from the previous step. Therefore, the change in internal energy is:

c. Change in Internal Energy:
ΔU = q - w
ΔU = 1.430 kJ - (work done)

Finally, to find the final volume of the gas, we need more information. We can use the ideal gas law and rearrange it to solve for V:

V = nRT / P

Since we already know n, R, P, and the final temperature from the previous calculations, we can substitute the values and find the final volume:

d. Final Volume:
V = (1.20 mol * 0.0821 atm L / (mol K) * (final temperature)) / 0.966 atm

To solve this problem, we will use the ideal gas law and the first law of thermodynamics.

a. To calculate the final temperature of the gas, we can use the equation:

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. Since the pressure (P), number of moles (n), and volume (V) are constant, we can rearrange the equation to solve for the final temperature (Tf) using the initial temperature (Ti) and the heat added (q):

Tf = Ti + q / (nR),

where q is the heat added to the system. We are given the initial temperature (Ti = 25 °C = 298 K) and the heat added (q = 1.430 kJ = 1430 J).

Substituting the values into the equation, we have:

Tf = 298 K + 1430 J / (1.20 mol * 8.314 J/(mol*K)).

Calculating this gives us the final temperature of the gas.

b. To calculate the work done by the gas, we can use the equation:

W = -PΔV,

where W is the work done, P is the pressure, and ΔV is the change in volume. In this case, the pressure is constant and the volume increases. Therefore, the equation simplifies to:

W = -P * Vf,

where Vf is the final volume of the gas. We need to find the final volume of the gas to calculate the work done.

c. To calculate the change in internal energy of the gas (ΔU), we can use the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system:

ΔU = q - W.

We already know the value of q from the given information. Now we need to calculate the work done (W) to determine the change in internal energy.

d. Finally, to calculate the final volume of the gas (Vf), we need to use the ideal gas law equation and rearrange it to solve for V:

V = nRT / P,

where n is the number of moles, R is the ideal gas constant, and T is the temperature. We can use the final temperature (Tf) that we calculated earlier to find the final volume of the gas.

Once we have calculated all these values, we will have the answers to the given questions.