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Current Question (ID: 11084)

Question:

$\text{A cyclic process for 1 mole of an ideal gas is shown in the } V-T \text{ diagram. The work done in } AB, BC \text{ and } CA \text{ respectively is:}$

Options:

1. $0, RT_2 \ln \left(\frac{V_1}{V_2}\right), R(T_1 - T_2)$
2. $R(T_1 - T_2), 0, RT_1 \ln \frac{V_1}{V_2}$
3. $0, RT_2 \ln \left(\frac{V_2}{V_1}\right), R(T_1 - T_2)$ (Correct)
4. $0, RT_2 \ln \left(\frac{V_2}{V_1}\right), R(T_2 - T_1)$

Solution:

$\text{Process } AB \text{ is isochoric,}$ $\therefore W_{AB} = P \Delta V = 0$ $\text{Process } BC \text{ is isothermal}$ $\therefore W_{BC} = RT_2 \ln \left(\frac{V_2}{V_1}\right)$ $\text{Process } CA \text{ is isobaric}$ $\therefore W_{CA} = P\Delta V = R\Delta T = R(T_1 - T_2)$

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
}