Import Question JSON

Current Question (ID: 8277)

Question:

$\text{An ideal gas absorbs 2000 cal of heat from a heat reservoir and does mechanical work equivalent to 4200 J. The change in internal energy of the gas is:}$

Options:

1. $\text{3000 cal}$
2. $\text{2000 cal}$
3. $\text{1500 cal}$
4. $\text{1000 cal}$

Solution:

$\text{Hint: } \Delta U = Q - W$ $\text{Step 1:}$ $\text{The change in internal energy } \Delta U \text{ is related to heat (Q) and work terms (W) according to}$ $\Delta U = Q - W$ $\text{Calculate the internal energy is as follows:}$ $\text{Heat absorbed is 2000 cal}$ $\text{Convert it into joule as follows:}$ $\text{2000 cal} \times 4.2 = 8400 \text{ joule}$ $\text{Step 2:}$ $\text{Out of this 4200 J energy is used in work done}$ $\Delta U = 8400 - 4200 = 4200 \text{ J}$ $\text{In calories is as follows:}$ $4200/4.2 = 1000 \text{ cal}$

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
}