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Current Question (ID: 19666)

Question:

$\text{An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity } C \text{ remains constant. If during this process the relation of pressure } P \text{ and volume } V \text{ is given by } PV^n = \text{ constant, then } n \text{ is given by: (here } C_P \text{ and } C_V \text{ are molar specific heat at constant pressure and constant volume, respectively)}$

Options:

1. $n = \frac{C_P}{C_V - C_P}$
2. $n = \frac{C - C_V}{C_P - C}$
3. $n = \frac{C - C_V}{C - C_P}$
4. $n = \frac{C - C_P}{C - C_V}$

Solution:

$\text{Hint: } C = C_v + \frac{PdV}{ndT}$ $C = C_v + \frac{PdV}{ndT} = \frac{R}{y-1} + \frac{R}{1-n}$ $C = \frac{R}{\frac{c_p}{c_v} - 1} + \frac{R}{1-n}$ $\text{on solving}$ $n = \frac{C - C_P}{C - C_V}$

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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
}