Import Question JSON

Current Question (ID: 21024)

Question:

$\text{What is the change in internal energy for 5 moles of an ideal gas when it undergoes reversible compression from 100 K to 200 K?}$ $\text{(Given } C_V = 28 \text{ J K}^{-1} \text{ mol}^{-1})$

Options:

1. $\Delta U = 8 \text{ kJ}$
2. $\Delta U = 14 \text{ kJ}$
3. $\Delta U = 10 \text{ kJ}$
4. $\Delta U = 2.8 \text{ kJ}$

Solution:

$\text{Hint: } \Delta U = n C_V \Delta T$ $\text{Calculate the value of } \Delta U \text{ as follows:}$ $\Delta U = n C_V \Delta T$ $= 5 \times 28 \times 100$ $= 14000 \text{ J} = 14 \text{ kJ}$

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
}