Chapter 17, Problem 5STP

Interpretation Introduction

Interpretation: The temperature of the alcohol increases by what amount is to be determined.

Concept Introduction: The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity.

Mathematically it is represented by

  $\text{Q=m×C×ΔT}$

  $\text{Q}$ = Heat absorbed or released

  $\text{m}$ = mass of the substance

  $\text{C}$ = heat capacity of the substance

  $\text{ΔT}$ = change in temperature

Answer to Problem 5STP

Increases $4.5°\text{C}$

Explanation of Solution

The heat absorbed by alcohol will be equal to the heat released by silver.

It is given that the heat capacity of ethanol is ten times larger than the heat capacity of silver.

Thus, ${\text{C}}_{\text{alc}}=10\times {\text{C}}_{\text{sil}}$

  ${\text{m}}_{\text{alc}}{\text{= m}}_{{}_{\text{sil}}}\text{= 55g}$

Putting in the values, we get:

  $\begin{array}{l}{\text{m}}_{\text{eth}}{\text{×C}}_{\text{eth}}\text{×(}\Delta {\text{T}}_{\text{eth}}{\text{)=-[m}}_{{}_{\text{sil}}}{\text{×C}}_{\text{sil}}\text{×(}\Delta {\text{T}}_{\text{sil}}\text{)]}\\ \text{55g×}10\times {\text{C}}_{\text{sil}}\text{×(}\Delta {\text{T}}_{\text{eth}}{\text{)=-[55g×C}}_{\text{sil}}\text{×-45}°\text{C]}\\ \Delta {\text{T}}_{\text{eth}}=+4.5°\text{C}\end{array}$