Thermodynamics and Thermochemistry - Result Question 83
####8. For silver, $C _p\left(J K^{-1} mol^{-1}\right)=23+0.01 T$. 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
(a) $62 kJ$
(b) $16 kJ$
(c) $21 kJ$
(d) $13 kJ$
(2019 Main, 8 April I)
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Solution:
- According to Kirchoff’s relation,
$$ \Delta H=n \int _{T _1}^{T _2} C _p d T $$
where, $\Delta H=$ Change in enthalpy.
$C _p=$ Heat capacity at constant pressure.
Thermodynamics and Thermochemistry 113
Given, $n=3$ moles, $T _1=300 K, T _2=1000 K, C _p=23+0.01 T$ On substituting the given values in Eq. (i), we get
$$ \begin{aligned} \Delta H & =3 \int _{300}^{1000}(23+0.01 T) d T=3 \int _{300}^{1000} 23 d T+0.01 T d T \ & =3\left[23 T+\frac{0.01 T^{2}}{2}\right] _{300}^{1000} \ & =3\left[23(1000-300)+\frac{0.01}{2}\left(1000^{2}-300^{2}\right)\right] \ & =3[16100+4550]=61950 J \approx 62 kJ \end{aligned} $$
