Let's answer the given questions step-by-step:
### Question Part (i): Maximum Temperature Gain
Given three substances with specific heat capacities:
- Substance A: [tex]\(2100 \, \text{J/kg} ^\circ \text{C}\)[/tex]
- Substance B: [tex]\(910 \, \text{J/kg} ^\circ \text{C}\)[/tex]
- Substance C: [tex]\(138 \, \text{J/kg} ^\circ \text{C}\)[/tex]
The specific heat capacity determines how much heat is required to change the temperature of a substance. When equal masses of these substances are heated with equal amounts of heat, the substance with the lowest specific heat capacity will experience the highest temperature change, because it requires less heat to increase its temperature by 1°C.
Therefore, Substance C with [tex]\(138 \, \text{J/kg} ^\circ \text{C}\)[/tex] will gain the maximum temperature.
### Question Part (ii): Suitable for Cooling and Heating Purposes
For a substance to be suitable for cooling and heating purposes, it should have a high specific heat capacity. A high specific heat capacity means the substance can absorb or release a large amount of heat without undergoing a significant change in temperature. This characteristic is essential for maintaining stable temperatures during cooling and heating processes.
Among the given substances, Substance A has the highest specific heat capacity of [tex]\(2100 \, \text{J/kg} ^\circ \text{C}\)[/tex], making it the most suitable for cooling and heating purposes.
### Question Part (iii): Fastest Cooling
When equal masses of substances A and B are taken at [tex]\(80^\circ \text{C}\)[/tex] and left to cool, the substance with the lower specific heat capacity will cool down faster. This is because a substance with a lower specific heat capacity loses temperature more quickly since less heat is required to change its temperature.
Substance B has a lower specific heat capacity of [tex]\(910 \, \text{J/kg} ^\circ \text{C}\)[/tex] compared to Substance A's [tex]\(2100 \, \text{J/kg} ^\circ \text{C}\)[/tex]. Therefore, Substance B will cool down faster.
### Question Part (iv): Suitable as a Thermometric Liquid
A good thermometric liquid should have a low specific heat capacity. This allows it to show significant temperature changes even with small amounts of absorbed or released heat, making it sensitive and responsive for measuring temperature differences.
Among the given substances, Substance C has the lowest specific heat capacity of [tex]\(138 \, \text{J/kg} ^\circ \text{C}\)[/tex]. Therefore, Substance C is the most suitable for use as a thermometric liquid.
