Import Question JSON

$\text{Hint: } W = -P\Delta V$ $\text{Step 1: Analyze the P-V diagram}$ $\text{Looking at the P-V diagram, we can observe that:}$ $\text{• The process starts at volume } V_i \text{ and ends at volume } V_f$ $\text{• The volume increases during the process } (V_i < V_f)$ $\text{• The pressure decreases as the volume increases}$ $\text{• The process follows a curved path, which appears to be a reversible expansion}$ $\text{Step 2: Determine the type of process and the work}$ $\text{This is an expansion process, as the volume increases from } V_i \text{ to } V_f$. $\text{In thermodynamics, work is calculated as the area under the curve in a P-V diagram:}$ $W = \int_{V_i}^{V_f} P \, dV$ $\text{The area under the curve in the given P-V diagram represents the work done during the process.}$ $\text{Step 3: Apply the sign convention}$ $\text{According to the thermodynamic sign convention:}$ $\text{• Work done BY the system on the surroundings is negative}$ $\text{• Work done ON the system by the surroundings is positive}$ $\text{Since this is an expansion process } (V_i < V_f) \text{, the system is doing work on the surroundings.}$ $\text{We can also use the simplified formula: } W = -P\Delta V$ $\text{Since } \Delta V = V_f - V_i > 0 \text{ for expansion, and with the negative sign in the formula, the work is negative.}$ $\text{The negative sign in the formula represents the convention that work done by the system is negative.}$ $\text{Step 4: Verify the conclusion}$ $\text{The area under the P-V curve represents the work done by the system during expansion.}$ $\text{According to thermodynamic conventions, this work is negative.}$ $\text{Therefore, the work done as shown by the graph is negative.}$