To calculate the work done by the gas during this expansion, we can use the equation for work done by an ideal gas:

W = PΔV

Where:
- W is the work done by the gas
- P is the pressure of the gas
- ΔV is the change in volume of the gas

First, we need to calculate the change in volume of the gas. Since the process is reversible, we can use the ideal gas law:

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 (8.314 J/(mol·K))
- T is the temperature of the gas

Rearranging the equation, we get:

V = (nRT)/P

Since we know the initial and final pressures, we can calculate the initial and final volumes using the ideal gas law:

V_initial = (nRT_initial)/P_initial
V_final = (nRT_final)/P_final

Since the temperature remains constant, T_initial = T_final, and we can simplify the equations:

V_initial = (nRT_initial)/P_initial
V_final = (nRT_initial)/P_final

To find the change in volume, we can subtract the initial volume from the final volume:

ΔV = V_final - V_initial
= (nRT_initial)/P_final - (nRT_initial)/P_initial
= (nRT_initial)(1/P_final - 1/P_initial)

To calculate the number of moles of the gas, we can use the ideal gas law:

PV = nRT

Rearranging the equation, we get:

n = PV/(RT)

Plugging in the initial pressure, temperature, and volume into the equation, we get:

n = (2 bar)(0.1 kg)/(8.314 J/(mol·K))(300 K)
= 0.006073 moles

Now we can calculate the change in volume using the equation:

ΔV = (nRT_initial)(1/P_final - 1/P_initial)
= (0.006073 mol)(8.314 J/(mol·K))(300 K)(1/1 bar - 1/2 bar)
= 1.814 J

Finally, we can calculate the work done by the gas using the equation:

W = PΔV
= (1 bar)(1.814 J)
= 1.814 J

Therefore, the work done by the gas during this expansion is 1.814 J.

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