We start with 5.00 moles of an ideal monatomic gas with an initial temperature of 123C. The gas expands and, in the process, absorbs an amount of heat equal to 1300J and does an amount of work equal to 2040J.

The change in internal energy (U) is equal to heat in (Q) minus work out (W).

The key to this probloem is knowing that the internal energy per mole of a MONATOMIC gas is (3/2) R T.

Thus,
delta Q = (3/2)*n* R*(delta T)
= 1300 - 2040 = -740 J

n is the number of moles and R = 8.317 J/mole K

Solve for delta T. It will be negative. I get -12 C (or K)

Hey thanks! At one point I was using (3/2)R(deltaT) but I wasn't setting it equal to (DeltaQ).

To find the final temperature of the gas, we can use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat absorbed by the system minus the work done by the system.

The equation for the First Law of Thermodynamics is:
ΔU = Q - W

Where:
ΔU is the change in internal energy
Q is the heat absorbed by the system
W is the work done by the system

In this case, the equation becomes:
ΔU = 1300J - 2040J

Since we are dealing with an ideal monatomic gas, the change in internal energy can be expressed as:
ΔU = (3/2) n R ΔT

Where:
n is the number of moles
R is the ideal gas constant
ΔT is the change in temperature

We can equate the two equations:
(3/2) n R ΔT = 1300J - 2040J

First, let's find the change in temperature (ΔT). We can rearrange the equation as follows:
ΔT = (1300J - 2040J) / ((3/2) n R)

Substituting the given values:
n = 5.00 moles
R = 8.3145 J/(mol*K)

ΔT = (1300J - 2040J) / ((3/2) * 5.00 * 8.3145 J/(mol*K))

Now, let's calculate ΔT to find the change in temperature.

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

Q = ΔU + W

where:
Q is the heat absorbed by the gas,
ΔU is the change in internal energy of the gas, and
W is the work done by the gas.

The change in internal energy, ΔU, for a monatomic ideal gas can be calculated using the equation:

ΔU = (3/2) * n * R * ΔT

where:
n is the number of moles of gas,
R is the ideal gas constant, and
ΔT is the change in temperature.

The work done by the gas, W, can be calculated using the equation:

W = -P * ΔV

where:
P is the pressure of the gas, and
ΔV is the change in volume.

In this case, we are given the heat absorbed (Q = 1300J) and the work done (W = 2040J). We need to find the final temperature (Tf).

Let's break down the problem step by step:

1. Convert the initial temperature from Celsius to Kelvin:
Ti = 123°C = (123 + 273.15) K
Ti = 396.15 K

2. Since we are given the number of moles (n = 5.00 mol), ideal gas constant (R = 8.3145 J/(mol*K)), and the heat absorbed (Q = 1300 J), we can rearrange the equation Q = ΔU + W to solve for the change in internal energy (ΔU).

ΔU = Q - W
ΔU = 1300 J - 2040 J
ΔU = -740 J

3. Now, substitute the known values into the equation for the change in internal energy (ΔU) and solve for the change in temperature (ΔT).

ΔU = (3/2) * n * R * ΔT

-740 J = (3/2) * 5.00 mol * 8.3145 J/(mol*K) * ΔT

-740 J = 62.1825 J/K * ΔT

ΔT = -740 J / 62.1825 J/K
ΔT ≈ -11.89 K

Note: A negative change in temperature indicates a decrease in temperature.

4. Finally, calculate the final temperature (Tf) using the initial temperature (Ti) and the change in temperature (ΔT).

Tf = Ti + ΔT
Tf = 396.15 K - 11.89 K
Tf ≈ 384.26 K

Therefore, the final temperature of the gas is approximately 384.26 K.