Import Question JSON

Current Question (ID: 11053)

Question:

$\text{An ideal monoatomic gas } \left(\gamma = \frac{5}{3}\right) \text{ absorbs 50 cal in an isochoric process. The increase in internal energy of the gas is:}$

Options:

1. $20 \text{ cal}$
2. $\text{Zero}$
3. $50 \text{ cal}$ (Correct)
4. $30 \text{ cal}$

Solution:

$\text{Hint: In the isochoric process, work done = 0}$ $\text{Step 1: Find the heat absorbed and work done}$ $\Delta Q = 50 \text{ cal}$ $W = 0$ $\text{Step 2: Find the change in internal energy by using the first law of thermodynamics}$ $\Delta Q = \Delta U + W$ $\Delta U = \Delta Q$ $= 50 \text{ cal}$

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
}