Import Question JSON

Current Question (ID: 19706)

Question:

$\text{A diatomic gas is taken from point } A \text{ to point } B \text{ in a thermodynamic}$ $\text{process as described in the pressure-volume graph shown. The change in}$ $\text{internal energy is equal to:}$

Options:

1. $3.75 \times 10^6 \text{ J}$
2. $2.25 \times 10^6 \text{ J}$
3. $7.5 \times 10^6 \text{ J}$
4. $4.5 \times 10^6 \text{ J}$

Solution:

$\text{Hint: } \Delta U = nC_V \Delta T$ $\text{Step 1: Find the change in the internal energy of the gas in terms}$ $\text{of pressure and volume.}$ $\Delta U = \frac{f}{2} nR \Delta T$ $= \frac{f}{2} \Delta (PV)$ $\text{Step 2: Find the change in the internal energy of the gas.}$ $\Delta U = \frac{5}{2} \times (4000 - 2500) \times 10^3 \text{ J}$ $= \frac{5}{2} \times 1500 \times 10^3 \text{ J}$ $= \frac{7500 \times 10^3}{2} \text{ J}$ $= 3.75 \times 10^6 \text{ J}$

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
}