Chapter 6, Problem 6.46P

Interpretation Introduction

Interpretation:

The specific heat capacity of the $30.5\text{g}$ alloy at $93.0°\text{C}$ that is placed into $50.0\text{g}$ of water at $22.0°\text{C}$ in an insulated coffee-cup calorimeter with a heat capacity of $9.2\text{ J/K}$ is to be determined.

Concept introduction:

Calorimeter is a device that is employed to measure the heat absorbed or released by the system. Calorimeter is of two types:

1. Coffee cup calorimeter

2. Bomb calorimeter

Coffee cup calorimeter is employed to determine the heat absorbed or released by the substance placed in it at constant pressure. Coffee cup calorimeter is generally used in case of solid that does not dissolved in water. The heat released by the solid is gained by the water and calorimeter.

$-q_{\text{solid}}=q_{\text{water}}+q_{\text{calorimeter}}$

Specific heat capacity $\left(c\right)$ of a substance is the amount of heat needed to raise the temperature of $1\text{g}$ of a substance by $1\text{K}$. The formula to calculate heat required is as follows:

$q=\left(\text{mass}\right)\left(c\right)\left(\Delta T\right)$

Here,

$\Delta T$ is the temperature difference.

$q$ is the heat released or absorbed.

$c$ is the specific heat capacity of the substance.

The formula to calculate heat required in case of calorimeter is as follows:

$q_{\text{calorimeter}}=\left(C_{\text{calorimeter}}\right)\left(\Delta T\right)$

Here,

$\Delta T$ is the temperature difference.

$q_{\text{calorimeter}}$ is the heat released or absorbed by calorimeter.

$C_{\text{calorimeter}}$ is the specific heat capacity of the calorimeter.