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  4. For silver, Cp(JK-1 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 Δ H will be close to

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Q. For silver, $C_{p}(JK^{-1} mol^{-1}) = 23 + 0.01T$. 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

JEE MainJEE Main 2019Thermodynamics

Solution:

$\Delta H =n \int\limits^{T_{2}}_{T_1} C_{p,m} dT = 3 \times\int^{1000}_{300} \left(23+0.01T\right)dT $
$ = 3\left[23\left(1000-300\right)+ \frac{0.01}{2} \left(1000^{2} - 300^{2}\right)\right]$
$ = 61950 J \approx 2 kJ$