Import Question JSON

Current Question (ID: 11075)

Question:

$\text{A gas is taken through the cycle } A \rightarrow B \rightarrow C \rightarrow A\text{, as shown in the figure. What is the total amount of work done by the gas?}$

Options:

1. $1000 \text{ J}$ (Correct)
2. $\text{zero}$
3. $-2000 \text{ J}$
4. $2000 \text{ J}$

Solution:

$\text{Hint: Use } W = P dV$ $\text{Step: Find the total work done by the gas.}$ $\text{In cyclic processes, Net work done = Area under the P-V graph = Area of } \triangle ABC$ $\text{The work done in a process is positive if the process is clockwise, otherwise negative. Here, the process is clockwise. Therefore, net work done = area under the P-V curve.}$ $\Rightarrow W = (4 \times 10^5 \times 5 \times 10^{-3})/2 = 1000 \text{ J}$ $\text{Hence, option (1) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}