Import Question JSON

Current Question (ID: 11030)

Question:

$\text{If } n \text{ moles of an ideal gas is heated at a constant pressure from } 50°\text{C to } 100°\text{C, the increase in the internal energy of the gas will be:}$ $\left(\frac{C_p}{C_v} = \gamma \text{ and } R = \text{gas constant}\right)$

Options:

1. $\frac{50nR}{\gamma - 1}$ (Correct)
2. $\frac{100nR}{\gamma - 1}$
3. $\frac{50n\gamma R}{\gamma - 1}$
4. $\frac{25n\gamma R}{\gamma - 1}$

Solution:

$\text{Hint: } \Delta U = nC_V\Delta T$ $\text{Step: Find the increase in the internal energy of the gas.}$ $\text{For } n \text{ moles of an ideal gas, the increase in internal energy } \Delta U \text{ is given by,}$ $\Delta U = nC_V\Delta T$ $R = C_p - C_V$ $C_V = \frac{R}{\gamma - 1}$ $\Delta U = nC_V\Delta T = n \left(\frac{R}{\gamma - 1}\right) \times 50$ $\Rightarrow \Delta U = \frac{50nR}{\gamma - 1}$ $\text{Hence, option (1) is the correct answer.}$

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
}