Question:

A gas undergoes a thermodynamic process where its temperature is raised from $T_i = 300 \, \text{K}$ to $T_f = 600 \, \text{K}$, while the pressure remains constant at $P = 2 \, \text{atm}$. The gas is contained in a container with a volume of $V = 5 \, \text{m}^3$. Given that the molar mass of the gas is $M = 28 \, \text{g/mol}$, calculate the work done by the gas during this process.

Answer:

The work done by the gas in a thermodynamic process can be calculated using the equation:

Where:

• $W$ is the work done by the gas,
• $P$ is the pressure,
• $\Delta V$ is the change in volume.

In this case, the pressure remains constant at $P = 2 \, \text{atm}$, and the initial volume is $V_i = 5 \, \text{m}^3$. To calculate the change in volume, we need to find the final volume $V_f$.

At constant pressure, the relationship between pressure, volume, and temperature is given by:

Rearranging the equation, we can solve for $V_f$:

Substituting the given values:

Now, we can calculate the change in volume:

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

To convert atm to SI units (Joules), we need to multiply by the conversion factor: $1 \, \text{atm} = 101.325 \, \text{J/m}^3$.

Therefore, the work done by the gas during this process is 1013.25 J.