Import Question JSON

Current Question (ID: 19683)

Question:

$\text{In a certain thermodynamical process, the pressure of a gas depends on its volume as } kV^3. \text{ The work done when the temperature changes from } 100^\circ\text{C to } 300^\circ\text{C will be:}$ $\text{(where } n \text{ denotes number of moles of a gas)}$

Options:

1. $20nR$
2. $30nR$
3. $40nR$
4. $50nR$

Solution:

$\text{Hint: } W = \int PdV$ $\text{Step: Find the work done when the temperature changes from } 100^\circ\text{C to } 300^\circ\text{C.}$ $\text{Given: } P = kV^3$ $\Rightarrow PV^{-3} = \text{Constant}(K)$ $\therefore \gamma = -3.$ $\text{The work done is given by:}$ $\Rightarrow W = \frac{nR(T_1 - T_2)}{\gamma - 1} = \frac{nR(100 - 300)}{-3 - 1}$ $\Rightarrow W = \frac{200nR}{4} = 50nR$ $\text{Hence, option (4) is the correct answer.}$

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
}