Import Question JSON

Current Question (ID: 11029)

Question:

$\text{The incorrect relation is:}$ $\text{(where symbols have their usual meanings)}$

Options:

1. $C_P = \frac{\gamma R}{\gamma - 1}$
2. $C_P - C_V = R$
3. $\Delta U = \frac{P_f V_f - P_i V_i}{1 - \gamma}$ (Correct)
4. $C_V = \frac{R}{\gamma - 1}$

Solution:

$\text{Hint: Use the concept of the adiabatic process.}$ $\text{Step: Find the incorrect relation.}$ $\text{For the adiabatic process, } \Delta Q = 0$ $\text{According to the first law of thermodynamics;}$ $dQ = \Delta U + dW$ $\Rightarrow \Delta U = -W$ $\Rightarrow \Delta U = \frac{P_f V_f - P_i V_i}{\gamma - 1}$ $\left[W = \frac{P_f V_f - P_i V_i}{1 - \gamma}\right]$ $\text{Hence, option (3) is the correct answer.}$

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
}