Import Question JSON

Current Question (ID: 19690)

Question:

$\text{A thermally insulated vessel contains an ideal gas of molecular mass } M \text{ and a specific heat ratio of } 1.4. \text{ The vessel is moving with speed } v \text{ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, then the vessel temperature of the gas increases by: } (R = \text{universal gas constant})$

Options:

1. $\frac{Mv^2}{7R}$
2. $\frac{Mv^2}{5R}$
3. $\frac{2Mv^2}{7R}$
4. $\frac{7Mv^2}{5R}$

Solution:

$\text{Hint: } \Delta U = Q - W$ $\text{Step: Find the increase in temperature of the vessel.}$ $\text{When the vessel is suddenly brought to rest, the kinetic energy of the vessel (and the gas molecules inside) will be converted into the internal energy of the gas, which increases its temperature.}$ $\frac{1}{2} Mv^2 = \Delta U$ $\Rightarrow \frac{1}{2} Mv^2 = \frac{f}{2} R \Delta T$ $\Rightarrow \Delta T = \frac{Mv^2}{fR}$ $\Rightarrow \Delta T = \frac{Mv^2}{5R} \quad [f = 5, \text{ For diatomic molecule}]$ $\text{Hence, option (2) is the correct answer.}$

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
}