10. Two solid substances of equal mass are heated with the same power input. The graph below shows how the temperatures of the substances vary with time during heating.
Which of the following statements are correct?
I. Substance A has a lower specific heat capacity than Substance B when they are in the same physical state.
II. The specific heat capacity of each substance is lower in the solid state than the liquid state.
III. Substance AA has a lower specific latent heat of fusion than Substance B.
A
Explanation:
The energy E required to completely melt each substance is given by
where mm is the mass of the substance and L is the specific latent heat of fusion.
Therefore, for a given power P, the duration tmelt of the plateau obeys the equation
tmelt=mL/P
The two substances have equal values of mm and P, meaning that since Substance A has a higher tmelt value than Substance B, it also possesses a higher L value. Hence, Statement III is incorrect.
The rates of temperature change before and after melting are related to the specific heat capacity c via the expression
- E = mcΔT
- PΔt=mcΔT
- ΔTΔt=Pmc
The gradient of the graph is therefore inversely proportional to cc.
In both solid and liquid state, Substance A exhibits a higher value of ΔTΔt than Substance B, meaning that has a lower value of c. Hence, Statement I is correct.
Furthermore, for each substance, the gradient of the graph is lower in the liquid phase than in the solid phase, which means that after melting cc increases and Statement II is correct.