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Current Question (ID: 11079)

Question:

$\text{An ideal gas is taken through the cycle } A \rightarrow B \rightarrow C \rightarrow A \text{ as shown in the figure below. If the net heat supplied to the gas is 10 J, then the work done by the gas in the process } B \rightarrow C \text{ is:}$

Options:

1. $-10 \text{ J}$ (Correct)
2. $-30 \text{ J}$
3. $-15 \text{ J}$
4. $-20 \text{ J}$

Solution:

$\text{Hint: } \Delta Q = \Delta U + \Delta W$ $\text{Step: Find the work done by the gas in the process } B \rightarrow C\text{.}$ $\text{According to the first law of thermodynamics, we get;}$ $\Delta Q = \Delta U + \Delta W$ $\Rightarrow \Delta Q = \Delta U + W_{AB} + W_{BC} + W_{CA}$ $\Rightarrow 10 = 10(3 - 1) + W_{BC} \quad [\Delta U = 0 \text{ for cyclic process, } W_{CA} = 0 \text{ [isochoric process]}]$ $\Rightarrow W_{BC} = 10 - 20 = -10 \text{ J}$ $\text{Hence, option (1) is the correct answer.}$

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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
}