A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.6 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $7.2 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are $600 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (solid), } 1000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (liquid), and } 400$ $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (gaseous). }$ How much heat is given up by 2.80 kg of this substance when it is cooled from $170 ^ { \circ } \mathrm { C } \text { to } 86 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

Question

A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.6 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is  $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $7.2 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific  heats for the solid, liquid, and gaseous phases are $600 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (solid), } 1000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (liquid), and } 400$ $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (gaseous). }$ How much heat is given up by  2.80 kg of this substance when it is cooled from $170 ^ { \circ } \mathrm { C } \text { to } 86 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

Quizplus · Accepted Answer

The heat given up by the substance as it cools from 170°C to 86°C involves cooling the gas from 170°C to 150°C, condensing it at 150°C, and then cooling the liquid from 150°C to 86°C. The heat lost during cooling in the gaseous phase is calculated using $q = mc\Delta T$, where $m = 2.80 \, \text{kg}$, $c = 400 \, \text{J/kg}\cdot\text{K}$ for the gas, and $\Delta T = 20\, \text{K}$ (from 170°C to 150°C). The heat of vaporization is given as $7.2 \times 10^4 \, \text{J/kg}$, which is the energy released when the gas condenses at 150°C. Finally, the heat lost while cooling the liquid from 150°C to 86°C is calculated with $m = 2.80 \, \text{kg}$, $c = 1000 \, \text{J/kg}\cdot\text{K}$ for the liquid, and $\Delta T = 64\, \text{K}$. Adding these three amounts of heat gives the total heat released.

A Substance Has a Melting Point Of 20∘C20 ^ { \circ } \mathrm { C }20∘C

A Substance Has a Melting Point Of $20 ^ { \circ } \mathrm { C }$