Import Question JSON

Current Question (ID: 19724)

Question:

$\text{A diatomic gas } (\gamma = 1.4) \text{ does } 400 \text{ J of work when it is expanded isobarically.}$ $\text{The heat given to the gas in the process is:}$

Options:

1. $1000 \text{ J}$
2. $1200 \text{ J}$
3. $1400 \text{ J}$
4. $1600 \text{ J}$

Solution:

$\text{Hint: Apply the first law of thermodynamics.}$ $\text{Step: Find the heat given to the gas.}$ $W = P \Delta V$ $\Rightarrow W = nR \Delta T = 400 \text{ J}$ $\Rightarrow Q = W + \Delta U$ $\Rightarrow Q = nR \Delta T + \frac{5}{2} nR \Delta T$ $\Rightarrow Q = nR \Delta T \left(1 + \frac{5}{2}\right)$ $\Rightarrow Q = \frac{400 \times 7}{2} = 1400 \text{ J}$ $\text{Hence, option (3) is the correct answer.}$

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
}