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Current Question (ID: 8294)

Question:
$\text{For the graph given below, it can be concluded that work done during the process shown will be-}$ $[\text{P-V diagram showing compression process from volume } V_i \text{ to } V_f \text{ with a stepped decrease in pressure}]$
Options:
  • 1. $\text{Zero}$
  • 2. $\text{Negative}$
  • 3. $\text{Positive}$
  • 4. $\text{Cannot be determined}$
Solution:
$\text{Hint: Compression process}$ $\text{Step 1: Analyze the P-V diagram}$ $\text{Looking at the P-V diagram, we can see that the volume is decreasing from } V_i \text{ (initial volume) to } V_f \text{ (final volume).}$ $\text{When volume decreases }(V_f < V_i)\text{, the process is a compression.}$ $\text{The diagram shows a stepped process with decreasing pressure, representing a non-ideal compression path.}$ $\text{Step 2: Determine the work done}$ $\text{The work done in a thermodynamic process can be calculated as the area under the curve in a P-V diagram:}$ $W = \int_{V_i}^{V_f} P \, dV$ $\text{For compression processes, the sign convention in thermodynamics is:}$ $\text{• Work done ON the system is positive}$ $\text{• Work done BY the system is negative}$ $\text{Since } V_f < V_i \text{, we have a compression process where the surroundings do work on the system.}$ $\text{We can also use the simplified formula for work:}$ $W = -P(V_f - V_i)$ $\text{Since } V_f < V_i\text{, the term } (V_f - V_i) \text{ is negative.}$ $\text{With the negative sign in front, the overall work becomes positive.}$ $\text{Step 3: Verify the conclusion}$ $\text{From the P-V diagram, we can visually confirm that work is being done ON the system (compression), which corresponds to positive work.}$ $\text{The area enclosed by the stepped path represents the work done, and in this case of compression, the work is positive.}$ $\text{Therefore, the work done during the process shown in the P-V diagram is positive.}$

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Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}