Thermodynamics And Thermochemistry
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Thermodynamics and Thermochemistry - Result Question 8
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
(2019 Main, 8 April I)
(a) $62 $ $kJ$
(b) $16 $ $kJ$
(c) $21 $ $kJ$
(d) $13 $ $kJ$
Show Answer
Answer:
Correct Answer: 8. (a)
Solution:
According to Kirchoff’s relation,
$\Delta H=n \int _{T _1}^{T _2} C _p d T \hspace{15mm}…(i)$
where, $\Delta H=$ Change in enthalpy.
$C _p=$ Heat capacity at constant pressure.
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
$\begin{aligned} \Delta H & =3 \int _{300}^{1000}(23+0.01 T) d T=3 \int _{300}^{1000} 23 d T+0.01 T d T \\ & =3\left[23 T+\frac{0.01 T^{2}}{2}\right] _{300}^{1000} \\ & =3\left[23(1000-300)+\frac{0.01}{2}\left(1000^{2}-300^{2}\right)\right] \\ & =3[16100+4550]=61950 J \approx 62 kJ \end{aligned}$
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