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Current Question (ID: 11024)

Question:

$\text{The PV diagram of an ideal gas is shown in the figure. The work done by the gas in the process } 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \text{ is given by:}$

Options:

1. $\frac{9}{2} P_0V_0$ (Correct)
2. $\frac{15}{2} P_0V_0$
3. $\frac{13}{2} P_0V_0$
4. $\frac{3}{2} P_0V_0$

Solution:

$\text{Hint: Work done is given by the area under the P-V graph.}$ $\text{Step 1: Identify the area.}$ $\text{As the process goes from } 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow 6 \rightarrow 1 \text{ as shown in the figure.}$ $\text{Step 2: Break the area into calculating parts.}$ $\text{Now we calculate the area of the shaded region.}$ $A = 3P_0(2V_0) - \frac{1}{2}(3P_0) \times V_0$ $= \frac{9}{2} P_0V_0$ $\text{Hence, option (1) is the correct answer.}$

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
}