JEE Main · 2019 · Shift-ImediumTHERMO-123

For silver, Cp\,(JK-1mol-1) = 23 + 0.01T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

For silver, $C_p\,(\text{JK}^{-1}\text{mol}^{-1}) = 23 + 0.01T$ . If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of $\Delta H$ will be close to:

Options

a
16 kJ
b
62 kJ
✓
c
13 kJ
d
21 kJ

Correct Answerb

62 kJ

Detailed Solution

🧠 Temperature-dependent $C_P$ : integrate over the range rather than using a single value When $C_P = a + bT$ , the enthalpy change is $\Delta H = n\int_{T_1}^{T_2}(a + bT)\,dT$ , not simply $n C_P \Delta T$ .

🗺️ Calculation $n = 3\,\text{mol}$ , $T_1 = 300\,\text{K}$ , $T_2 = 1000\,\text{K}$

$\Delta H = 3\int_{300}^{1000}(23 + 0.01T)\,dT = 3\left[23T + 0.005T^2\right]_{300}^{1000}$

At 1000 K: $23(1000) + 0.005(10^6) = 23000 + 5000 = 28000$

At 300 K: $23(300) + 0.005(9 \times 10^4) = 6900 + 450 = 7350$

$\Delta H = 3 \times (28000 - 7350) = 3 \times 20650 = 61950\,\text{J} \approx 62\,\text{kJ}$

$\boxed{\text{Answer: (b) 62 kJ}}$

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