Import Question JSON

Current Question (ID: 11063)

Question:

$\text{If } \Delta Q \text{ and } \Delta W \text{ represent the heat supplied to the system and the work done on the system, respectively, then the first law of thermodynamics can be written as: (where } \Delta U \text{ is the internal energy)}$

Options:

1. $\Delta Q = \Delta U + \Delta W$
2. $\Delta Q = \Delta U - \Delta W$ (Correct)
3. $\Delta Q = \Delta W - \Delta U$
4. $\Delta Q = -\Delta U - \Delta W$

Solution:

$\text{Step 1: For first law of thermodynamics:}$ $\Delta Q = \Delta U + \Delta W$ $\text{Heat is supplied to the system, so } \Delta Q \rightarrow \text{Positive}$ $\text{and work is done on the system, so } \Delta W \rightarrow \text{Negative}$ $\text{Hence, } +\Delta Q = \Delta U - \Delta W$

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
}