Import Question JSON

Current Question (ID: 11028)

Question:

$\text{If a gas changes volume from 2 litres to 10 litres at a constant temperature of 300 K, then the change in its internal energy will be:}$

Options:

1. $12 \text{ J}$
2. $24 \text{ J}$
3. $36 \text{ J}$
4. $0 \text{ J}$ (Correct)

Solution:

$\text{Hint: } \Delta U = nC_V\Delta T$ $\text{Step: Find the internal energy of the gas.}$ $\text{As the temperature of the gas is constant i.e., the process is isothermal.}$ $\text{The internal energy of the gas is given by,}$ $\Delta U = nC_V\Delta T$ $\Rightarrow \Delta U = 0 \quad [\Delta T = 0]$ $\text{Hence, option (4) is the correct answer.}$

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
}