Chapter 6.3, Problem 6.5BFP

Interpretation Introduction

Interpretation:

The initial temperature of $33.2\text{g}$ titanium metal part that is added to $75.0\text{g}$ of water in a coffee-cup calorimeter at $55.00°\text{C}$ and decreases the temperature of water to $49.30°\text{C}$ is to be determined.

Concept introduction:

A calorimeter is a device that is employed to measure the heat absorbed or released by the system. A 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 the calorimeter at constant pressure. Coffee cup calorimeter is generally used in case of solid that does not dissolve in water. The heat released by the solid is gained by the water when no heat escapes through calorimeter.

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

The formula to calculate the heat capacity of metal is as follows:

$c_{\text{metal}}=-\frac{\left(c_{{\text{H}}_{\text{2}}\text{O}}\right)\left({\text{mass}}_{{\text{H}}_{\text{2}}\text{O}}\right)\left(\Delta T_{{\text{H}}_{\text{2}}\text{O}}\right)}{\left({\text{mass}}_{\text{metal}}\right)\left(\Delta T_{\text{metal}}\right)}$        (1)

The formula to calculate $\Delta T$ of the system is as follows:

$\Delta T=T_{\text{Final}}-T_{\text{Initial}}$        (2)

The conversion factor to convert degree Celsius to Kelvin is as follows:

$T\left(\text{K}\right)=T\left(°\text{C}\right)+273.15$        (3)