A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.4 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $6.8 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ 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 $\text { J/kg } \cdot K \text { (gaseous). }$ How much heat is required to raise the temperature of 1.90 kg of this substance from $- 4 ^ { \circ } \mathrm { C } \text { to } 106 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

Question

A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.4 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is  $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $6.8 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ 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 $\text { J/kg } \cdot K \text { (gaseous). }$ How much heat is required to raise the temperature of 1.90 kg of this substance from $- 4 ^ { \circ } \mathrm { C } \text { to } 106 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

Quizplus · Accepted Answer

To calculate the total heat required, we need to consider the heat needed for each phase change and temperature change:  1. Heat to raise temperature from $-4^\circ C$ to $20^\circ C$ (solid phase):  $Q_1 = m \cdot c_{\text{solid}} \cdot \Delta T = 1.90 \, \text{kg} \cdot 600 \, \text{J/kg} \cdot \text{K} \cdot (20 - (-4)) \, \text{K} = 27360 \, \text{J}$  2. Heat for melting at $20^\circ C$:  $Q_2 = m \cdot \text{heat of fusion} = 1.90 \, \text{kg} \cdot 3.4 \times 10^4 \, \text{J/kg} = 64600 \, \text{J}$  3. Heat to raise temperature from $20^\circ C$ to $106^\circ C$ (liquid phase):  $Q_3 = m \cdot c_{\text{liquid}} \cdot \Delta T = 1.90 \, \text{kg} \cdot 1000 \, \text{J/kg} \cdot \text{K} \cdot (106 - 20) \, \text{K} = 163400 \, \text{J}$  Total heat $Q = Q_1 + Q_2 + Q_3 = 27360 + 64600 + 163400 = 255360 \, \text{J} = 255.36 \, \text{kJ}$  The closest answer is 260 kJ.

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

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