Problem $1(10pts)$

Enthalpy is an important thermodynamic property of a system. Technically, it is the sum of the

internal energy of the system plus the product of the pressure times the volume of the system.

However, since the pressure times volume term is small for most systems $($especially solids and

liquids$),$ the enthalpy is often used as a stand$-$in for the internal energy of the system. While it is

not possible to measure the internal energy of the system, we can measure the change in enthalpy

of the with respect to that of a reference system.

In the table below are empirically determined values for $h^{\text{'}},$ the molar enthalpy $($enthalpy of one

mole$)$ of hydrogen $(H_2)$ with respect to the enthalpy of the system at $298$ K $.$ Use Newton's

Divided Difference Polynomial interpolation to estimate the molar entropy of $H_2$ at $1400$ K with

respect to $298$ K $,$ to a convergence of ${}_s=0\mathrm{.}008\%.$

There is an NDDP example in the Topic $4$ Module on Canvas. Keep $5$ significant figures.Problem $1(10pts)$

Enthalpy is an important thermodynamic property of a system. Technically, it is the sum of the

internal energy of the system plus the product of the pressure times the volume of the system.

However, since the pressure times volume term is small for most systems $($especially solids and

liquids$),$ the enthalpy is often used as a stand$-$in for the internal energy of the system. While it is

not possible to measure the internal energy of the system, we can measure the change in enthalpy

of the with respect to that of a reference system.

In the table below are empirically determined values for $h^{\text{'}},$ the molar enthalpy $($enthalpy of one

mole$)$ of hydrogen $(H_2)$ with respect to the enthalpy of the system at $298$ K $.$ Use Newton's

Divided Difference Polynomial interpolation to estimate the molar entropy of $H_2$ at $1400$ K with

respect to $298$ K $,$ to a convergence of ${}_s=0\mathrm{.}008\%.$

There is an NDDP example in the Topic $4$ Module on Canvas. Keep $5$ significant figures.