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Current Question (ID: 10740)

Question:

$\text{A substance is in solid form at 0°C. The amount of heat added to this substance and its temperature are plotted in the following graph. If the relative specific heat capacity of the solid substance is 0.5, from the graph, the specific latent heat of the melting process is:}$ $\text{(Specific heat capacity of water = 1000 cal kg}^{-1} \text{K}^{-1}\text{)}$

Options:

1. $60000 \text{ cal kg}^{-1}$
2. $40000 \text{ cal kg}^{-1}$ (Correct)
3. $10000 \text{ cal kg}^{-1}$
4. $20000 \text{ cal kg}^{-1}$

Solution:

$\text{Hint: During the phase change temperature remains constant.}$ $\text{Step 1:}$ $C_{\text{water}} = 1000 \text{ cal / kg K}$ $\text{Relative specific heat capacity} = 0.5$ $\Rightarrow \frac{C_{\text{solid}}}{C_{\text{water}}} = 0.5$ $C_{\text{solid}} = 500 \text{ cal / kg K}$ $\text{Step 2:}$ $Q = MC_{\text{sol}} \Delta T$ $\frac{\Delta T}{Q} = \text{slope of AB}$ $\frac{\Delta T}{Q} = \frac{80}{800} = \frac{1}{M \times 500}$ $M = 0.02 \text{ kg}$ $\text{Step 3:}$ $\text{Now, } Q = 800 \text{ cal} = ML_f$ $L_f = \frac{800}{0.02} = 40000 \text{ cal / kg}$

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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
}