∆u =0 as temperature is constant all the heat will be converted into work done

Change in Internal Energy of Oxygen during Expansion

To determine the change in internal energy of one mole of oxygen gas during its expansion from a volume of 1L to 5L at a constant temperature of T=280K, we can use the ideal gas law and the equation for the change in internal energy.

1. Ideal Gas Law:
The ideal gas law states that the product of pressure and volume of an ideal gas is directly proportional to the number of moles and the temperature of the gas.
PV = nRT

Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas

2. Equation for Change in Internal Energy:
The change in internal energy (ΔU) of a gas can be calculated using the equation:
ΔU = q - w

Where:
ΔU is the change in internal energy
q is the heat transferred to the system
w is the work done by the system

3. Constant Temperature:
Since the expansion of the oxygen gas is occurring at a constant temperature (T=280K), we can assume that there is no heat transferred to or from the system (q=0). Therefore, the change in internal energy can be simplified to:
ΔU = -w

4. Work Done by the System:
The work done by the system can be calculated using the equation:
w = -PΔV

Where:
P is the pressure of the gas
ΔV is the change in volume of the gas

5. Calculation:
Given that the initial volume of the oxygen gas is 1L and the final volume is 5L, the change in volume (ΔV) is:
ΔV = Vfinal - Vinitial
ΔV = 5L - 1L
ΔV = 4L

Since the pressure (P) remains constant during the expansion, we can substitute the values into the equation for work done:
w = -PΔV
w = -P(4L)

6. Simplification:
To simplify the equation further, we need to express the pressure (P) in terms of the ideal gas law. Rearranging the ideal gas law equation, we have:
P = nRT/V

Substituting this expression for P into the equation for work done, we get:
w = -nRTΔV/V

7. Calculation of Change in Internal Energy:
Finally, substituting the value of work done (w) into the equation for change in internal energy (ΔU), we have:
ΔU = -w
ΔU = -(-nRTΔV/V)
ΔU = nRTΔV/V

8. Calculation:
Substituting the given values, we have:
ΔU = (1 mol)(8.314 J/mol·K)(280 K)(4 L)/(1 L)
ΔU = 9309.92 J

Therefore, the change in internal energy of one mole of oxygen gas during its expansion from 1L to 5L at a constant temperature of T=280K is 930