Question

The molar heat capacity of water at constant pressure P is $75{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$. When $1.0\mathrm{kJ}$of heat is supplied to $100\mathrm{g}$ of water which is free to expand, the increase in temperature of the water is:

Answer 1

Step 1: Molar heat capacity:

• "Molar heat capacity is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature."

Step 2: Formula for Molar heat capacity:

• Molar heat capacity can be expressed as:
• $\mathrm{q}=\mathrm{m}\times {\mathrm{C}}_{\mathrm{p}}\times ∆\mathrm{T}$, where $\mathrm{q}$ is the heat supplied, $\mathrm{m}$ is the molality, ${\mathrm{C}}_{\mathrm{p}}$ is the molar heat capacity at constant pressure and $∆\mathrm{T}$ is the change in temperature.

Step 3: Given information:

• ${\mathrm{C}}_{\mathrm{p}}=75{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$
• $\mathrm{q}=1\mathrm{kJ}=1000\mathrm{J}$
• ${\mathrm{m}}_{\mathrm{w}}=100\mathrm{g}$
• ${\mathrm{M}}_{\mathrm{w}}=18\mathrm{g}{\mathrm{mol}}^{-1}$

Step 4: Calculation for the increase in temperature:

$$\begin{gathered} \mathrm{q}=\mathrm{m}\times {\mathrm{C}}_{\mathrm{p}}\times ∆\mathrm{T} \\ 1000\mathrm{J}=\frac{100\mathrm{g}}{18\mathrm{g}{\mathrm{mol}}^{-1}}\times 75{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\times ∆\mathrm{T} \\ ∆\mathrm{T}=2.4\mathrm{K} \end{gathered}$$

Thus, the change in temperature or increases in temperature is $2.4\mathrm{K}$.