Methane (Considered to be an ideal gas) initially at $25°\mathrm{C}$ and $1$ bar pressure is heated at constant pressure until the volume has doubled. The variation of the molar heat capacity with absolute temperature is given by:

${\mathrm{C}}_{\mathrm{P}}=22.34+48.1\times {10}^{-3}\mathrm{T}$. where ${\mathrm{C}}_{\mathrm{P}}$ is in ${\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$. Calculate $∆\mathrm{U}$ in $\mathrm{kJ}$.

Oxygen is heated from $300\mathrm{K}$ to $600\mathrm{K}$ at a constant pressure of $1 \mathrm{bar}$. The molar heat capacity in ${\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$ for ${\mathrm{O}}_2$ is:

${\mathrm{C}}_{\mathrm{P}}=25.5+13.6\times {10}^{-3}\mathrm{T}-42.5\times {10}^{-7}{\mathrm{T}}^2$

What is the increases in molar entropy (in Joule)?

What would be the heat evolved (in kcal) if one gram equivalent of $\mathrm{NaOH}$ is added to one gram equivalent of ${\mathrm{NH}}_4\mathrm{Cl}$ solution ? Assume that ${\mathrm{NH}}_4\mathrm{OH}$ and $\mathrm{NaCl}$ are quantitatively obtained.