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Current Question (ID: 11156)

Question:

$\text{In the PV graph shown below for an ideal diatomic gas, the change in the internal energy is:}$

Options:

1. $\frac{3}{2}P(V_2 - V_1)$
2. $\frac{5}{2}P(V_2 - V_1)$ (Correct)
3. $\frac{3}{2}P(V_1 - V_2)$
4. $\frac{7}{2}P(V_1 - V_2)$

Solution:

$\text{Hint: } \Delta U = nC_v \Delta T$ $\text{Step 1: Find molar specific heat at constant volume } C_v.$ $C_v = \frac{R}{\gamma-1} = \frac{R}{\frac{7}{5}-1} = \frac{5R}{2}$ $\text{Step 2: Find the change in internal energy.}$ $\Delta U = nC_v \Delta T$ $= n\left(\frac{5R}{2}\right)\Delta T$ $= \frac{5}{2}(nR \Delta T)$ $= \frac{5}{2}(P \Delta V)$ $= \frac{5}{2}P(V_2 - V_1)$

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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
}