Import Question JSON

Current Question (ID: 19669)

Question:

$\text{The following figure shows two processes } A \text{ and } B \text{ for a gas. If } \Delta Q_A \text{ and } \Delta Q_B \text{ are the amount of heat absorbed by the system in two cases, and } \Delta U_A \text{ and } \Delta U_B \text{ are changes in internal energies, respectively, then:}$

Options:

1. $\Delta Q_A > \Delta Q_B, \ \Delta U_A > \Delta U_B$
2. $\Delta Q_A < \Delta Q_B, \ \Delta U_A < \Delta U_B$
3. $\Delta Q_A > \Delta Q_B, \ \Delta U_A = \Delta U_B$
4. $\Delta Q_A = \Delta Q_B, \ \Delta U_A = \Delta U_B$

Solution:

$\text{Hint: Internal energy is a state function.}$ $\text{Step: Find the relation between } \Delta Q_A \text{ and } \Delta Q_B. \text{ Initial and final points are the same therefore change in internal energy is also the same internal energy is the state function.}$ $\Delta U_A = \Delta U_B$ $\therefore \Delta W_A > \Delta W_B \ (\text{work done=area under the } P-V \text{ graph})$ $\Rightarrow \Delta Q_A > \Delta Q_B \ (\Delta Q = \Delta U + \Delta W)$ $\text{Hence, option (3) is the correct answer.}$

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
}