Question 164: Thermodynamics & KTG

Question

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$?

Accepted Answer

To determine the correct graph, we must analyse the phase changes and temperature changes that occur when heat is supplied to water starting from $-20^{\circ} \mathrm{C}$.
Step 1 :
Heating Ice ( $-20^{\circ} \mathrm{C}$ to $0^{\circ} \mathrm{C}$ )
Initially, the substance is ice. As heat is supplied, the temperature of the ice increases linearly from $-20^{\circ} \mathrm{C}$ to 0 ${ }^{\circ} \mathrm{C}$. This is represented by a sloping line on the graph.
$$ \mathrm{Q}_1=\mathrm{m}_{	ext {ice }} \mathrm{c}_{	ext {ice }}(\mathrm{T}+20) $$
Step 2 :
Melting (Phase Change at $0^{\circ} \mathrm{C}$ )
At $0{ }^{\circ} \mathrm{C}$, the ice begins to melt into water. During a phase change, the temperature remains constant even as heat is added (latent heat of fusion). This is represented by a horizontal line at $0^{\circ} \mathrm{C}$.
$$ Q_2=m_{i c e} L_f $$
Step 3 :
Heating Liquid Water ( $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ )
Once all the ice has melted, further heat increases the temperature of the liquid water linearly from $0^{\circ} \mathrm{C}$ up to its boiling point at $100^{\circ} \mathrm{C}$. This is another sloping line.
$$ \mathrm{Q}_3=\mathrm{m}_{	ext {water }} \mathrm{c}_{	ext {water }} \mathrm{T} $$
Step 4 :
Boiling (Phase Change at $100^{\circ} \mathrm{C}$ )
At $100^{\circ} \mathrm{C}$, the water begins to turn into steam. The temperature stays constant during this process (latent heat of vaporization). This is represented by a second horizontal line at $100^{\circ} \mathrm{C}$.
$$ \mathrm{Q}_4=\mathrm{m}_{	ext {water }} \mathrm{L}_{\mathrm{v}} $$
Step 5 :
Heating Steam ( $100^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$ )
After all the water has turned into steam, the temperature of the steam increases from $100^{\circ} \mathrm{C}$ toward $120^{\circ} \mathrm{C}$. This is represented by a final sloping line.
$$ \mathrm{Q}_5=\mathrm{m}_{	ext {vapour }} \mathrm{C}_{	ext {vapour }}(\mathrm{T}-100) $$
So, the correct graph must show :
1. A start point below $0^{\circ} \mathrm{C}$ (at $-20^{\circ} \mathrm{C}$ ).
2. A horizontal plateau at $0^{\circ} \mathrm{C}$ (melting).
3. A horizontal plateau at $100^{\circ} \mathrm{C}$ (boiling).
Hence, the correct option is (C).

Answer

Answer

Answer

Answer

Thermodynamics & KTG

Which of the following best represents the temperature versus heat supplied graph for water, in the range of -20^{\circ} \mathrm{C} to 120^{\circ} \mathrm{C}?

Choose the correct answer: