Chapter U5.98, Problem 6E

Interpretation Introduction

Interpretation: The amount of energy required to raise the temperature of $50\text{ g}$ of methanol from ${\text{20 }}^{\text{o}}{\text{C to 70 }}^{\text{o}}\text{C}$ needs to be calculated.

Concept Introduction: The relation between heat and change in temperature is given as:

  $\text{q = mc}\Delta \text{T}$

Where q is heat, m is mass, c is specific heat and $\Delta \text{T}$ is change in temperature.

Answer to Problem 6E

The amount of energy required to raise the temperature of $50\text{ g}$ of methanol from ${\text{20 }}^{\text{o}}{\text{C to 70 }}^{\text{o}}\text{C}$ is $\text{6325 J}$ .

Explanation of Solution

The value for the specific heat of methanol is $\text{2}{\text{.53 J/g}}^{\text{o}}\text{C}$ .

The change in temperature is calculated as:

  $\begin{array}{l}{\text{ΔT = T}}_{\text{final}}{\text{-T}}_{\text{initial}}\\ {\text{ΔT = 70 }}^{\text{o}}{\text{C - 20 }}^{\text{o}}\text{C}\\ {\text{ΔT = 50 }}^{\text{o}}\text{C}\end{array}$

The amount of energy in terms of heat required to raise the temperature of $50\text{ g}$ of methanol from ${\text{20 }}^{\text{o}}{\text{C to 70 }}^{\text{o}}\text{C}$ is calculated as:

  $\begin{array}{l}\text{q = 50 g}\times \text{2}{\text{.53 J/g}}^{\text{o}}\text{C}\times {\text{50 }}^{\text{o}}\text{C}\\ \text{q = 6325 J}\end{array}$

Thus, the amount of energy required to raise the temperature of $50\text{ g}$ of methanol from ${\text{20 }}^{\text{o}}{\text{C to 70 }}^{\text{o}}\text{C}$ is $\text{6325 J}$ .