Import Question JSON

Current Question (ID: 19692)

Question:

$\text{A sample of an ideal gas is taken through the cyclic process } ABC A \text{ as shown in the figure.}$ $\text{It absorbs, } 40 \text{ J of heat during part } AB, \text{ no heat during } BC, \text{ and rejects } 60 \text{ J of heat during } CA.$ $\text{A work of } 50 \text{ J is done on the gas during part } BC. \text{The internal energy of the gas at } A \text{ is } 1560 \text{ J.}$ $\text{The work done by the gas during the part } CA \text{ is:}$

Options:

1. $20 \text{ J}$
2. $30 \text{ J}$
3. $-30 \text{ J}$
4. $-60 \text{ J}$

Solution:

$\text{Hint: For a cyclic process, } \Delta U = 0$ $\text{Step: Find the work done by the gas during } CA.$ $\text{The net heat absorbed } = Q_{\text{net}} = +40 - 60 = -20 \text{ J}$ $\text{The total work done } = W_{\text{total}} = 0 - 50 + W_{CA}$ $\text{In the cyclic process, } \Delta U = 0$ $\Rightarrow \Delta Q = \Delta W$ $\Rightarrow -20 = -50 + W_{CA}$ $\Rightarrow W_{CA} = 30 \text{ J}$ $\text{Hence, option (2) is the correct answer.}$

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
}