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Current Question (ID: 11004)

Question:

$\text{The pressure and volume of a gas are changed as shown in the P-V diagram. The temperature of the gas will:}$

Options:

1. $\text{increase as it goes from A to B.}$ (Correct)
2. $\text{increase as it goes from B to C.}$
3. $\text{remain constant during these changes.}$
4. $\text{decrease as it goes from D to A.}$

Solution:

$\text{The relationship between pressure (P), volume (V), and temperature (T) for an ideal gas is given by the ideal gas equation:}\n\n\text{PV} = \text{nRT}\n\n\text{Where n is the number of moles and R is the ideal gas constant. For a fixed amount of gas, nR is constant, so PV is directly proportional to T.}\n\n\text{PV} \propto \text{T}\n\n\text{To determine the change in temperature, we need to analyze how the product PV changes along each path.}\n\n\text{Path A to B:}\n\text{This is an isobaric process, where pressure (P) is constant. The volume (V) increases from A to B. Since V increases and P is constant, the product PV increases. Thus, the temperature T increases.}\n\n\text{Path B to C:}\n\text{This is an isochoric process, where volume (V) is constant. The pressure (P) decreases from B to C. Since P decreases and V is constant, the product PV decreases. Thus, the temperature T decreases.}\n\n\text{Path C to D:}\n\text{This is an isobaric process, where pressure (P) is constant. The volume (V) decreases from C to D. Since V decreases and P is constant, the product PV decreases. Thus, the temperature T decreases.}\n\n\text{Path D to A:}\n\text{This is an isochoric process, where volume (V) is constant. The pressure (P) increases from D to A. Since P increases and V is constant, the product PV increases. Thus, the temperature T increases.}\n\n\text{Based on this analysis, the temperature increases as the gas goes from A to B, and also from D to A. The temperature decreases from B to C and from C to D.}\n\n\text{Let's check the given options:}\n\n\text{1. increase as it goes from A to B. (Correct)}\n\text{2. increase as it goes from B to C. (Incorrect, temperature decreases)}\n\text{3. remain constant during these changes. (Incorrect, temperature changes)}\n\text{4. decrease as it goes from D to A. (Incorrect, temperature increases)}\n\n\text{The only correct statement among the options is that the temperature increases from A to B.}$

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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
}