Import Question JSON

Current Question (ID: 11070)

Question:

$\text{An ideal gas is taken through the process as shown in the figure. Then:}$

Options:

1. $\text{In the process AB, the work done by the system is positive.}$
2. $\text{In process AB, heat is rejected out of the system.}$ (Correct)
3. $\text{In the process AB, internal energy increases.}$
4. $\text{In the process AB, internal energy decreases, and in the process BC, internal energy increases.}$

Solution:

$\text{Hint: In an isothermal process, the internal energy of the system is constant.}$ $\text{Step 1: Find the relation between } V_1, V_2 \text{ and } V_3.$ $\text{Ideal gas equation:}$ $PV = nRT$ $P = \frac{nRT}{V}$ $\text{Slope of P - T graph } \propto \frac{1}{V}$ $\Rightarrow V_3 < V_2 < V_1$ $\text{Step 2: Find values for AB,}$ $W < 0$ $\Delta U = 0 \text{ (as) temperature is constant}$ $\Delta Q = \Delta U + W$ $\Delta Q = W$ $\Rightarrow \Delta Q < 0 \text{ (as) } W < 0$

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
}