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Current Question (ID: 11015)

Question:

$\text{The pressure-temperature } (P-T) \text{ graph for two processes, } A \text{ and } B\text{, in a system is shown in the figure. If } W_1 \text{ and } W_2 \text{ are work done by the gas in process } A \text{ and } B \text{ respectively, then:}$

Options:

1. $W_1 = W_2$
2. $W_1 < W_2$
3. $W_1 > W_2$ (Correct)
4. $W_1 = -W_2$

Solution:

$\text{Hint: } W = \int P\Delta V$ $\text{Step 1: Identify the isochoric lines in the given } P-T \text{ graph and identify the } A \text{ and } B \text{ process.}$ $\text{According to Ideal Gas;}$ $PV = nRT$ $\Rightarrow P = \frac{nR}{V}T \ldots (1)$ $\text{Equation (1) represents a straight line } (y = mx) \text{ passing through the origin with slope } \frac{nR}{V}\text{. As } V \text{ increases, the slope of the } P-T \text{ curve decreases.}$ $\text{As pressure is constant for both processes, } A \text{ and } B \text{ therefore, } A \text{ and } B \text{ are isobaric processes.}$ $\text{Step 2: Compare the work done for processes } A \text{ and } B\text{.}$ $\text{The work done for the isobaric process is given by;}$ $W_{\text{isobaric}} = P\Delta V$ $W_1 = P_1\Delta V$ $W_2 = P_2\Delta V$ $\Rightarrow W_1 > W_2 \quad [P_1 > P_2]$ $\text{Hence, option (3) is the correct answer.}$

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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
}