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Current Question (ID: 11176)

Question:

$\text{The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from } T_1 \text{ K to } T_2 \text{ K is:}$

Options:

1. $\frac{3}{2} N_a k_B (T_2 - T_1)$
2. $\frac{5}{2} N_a k_B (T_2 - T_1)$
3. $\frac{3}{4} N_a k_B \frac{T_2}{T_1}$
4. $\frac{3}{8} N_a k_B (T_2 - T_1)$ (Correct)

Solution:

$\text{Hint: The amount of heat required depends on the specific heat capacity of the gas.}$ $\text{Step 1: Find the heat required.}$ $\Delta Q = nC_v \Delta T$ $= \frac{1}{4} \times \frac{3}{2}R(T_2 - T_1) \text{ (As) } n = \frac{1}{4}, C_v = \frac{3}{2}R$ $= \frac{3}{8}N_a k_B (T_2 - T_1)$

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
}