Chapter 4, Problem 4.6P

Interpretation Introduction

Interpretation:

To prove that error, E = ${\langle C_p\rangle }_H$ - C_P= $\frac{C}{12}{\left(T_1-T_2\right)}^2$

Concept Introduction:

The value of ${\langle C_p\rangle }_H$ can be calculated using the following equation:

${\displaystyle {\int }_{T_1}^{T_2}{C}_{p}dT=A{\displaystyle {\int }_{T_1}^{T_2}dT}+B{\displaystyle {\int }_{T_1}^{T_2}TdT}}+C{\displaystyle {\int }_{T_1}^{T_2}{T}^{2}dT}$

We calculate C_Pat T_meanto find the error resulting from the difference of ${\langle C_p\rangle }_H$ and C_P$T_{mean}=\frac{T_1+T_2}{2}$

$C_p=A+BT+C{T}^2$

Here, T is temperature and A, B and C are constants.