Import Question JSON

Current Question (ID: 19662)

Question:

$\text{One mole of a diatomic ideal gas undergoes a cyclic process } ABC \text{ as shown in figure. The process } BC \text{ is adiabatic. The temperatures at } A, B \text{ and } C \text{ are } 400 \text{ K, } 800 \text{ K and } 600 \text{ K respectively. Choose the correct statement:}$

Options:

1. $\text{The change in internal energy in the process } CA \text{ is } 700 R$
2. $\text{The change in internal energy in the process } AB \text{ is } -350 R$
3. $\text{The change in internal energy in the process } BC \text{ is } -500 R$
4. $\text{The change in internal energy in the whole cyclic process is } 250 R$

Solution:

$\Delta U = n C_V \Delta T$ $n = 1$ $C_V = \frac{5}{2} R$ $C_P = \frac{7}{2} R$ $BC - \text{ Adiabatic}$ $\Delta U_{CA} = n C_V \Delta T = \frac{5}{2} R \times (-200) = -500 R$ $\Delta U_{BC} = n C_V \Delta T = 1 \times \frac{5}{2} R (600 - 800)$ $\Delta U_{BC} = -500 R$

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
}