Answer :
Certainly! Let's work through the problem thoroughly.
### Given Table:
[tex]\[ \begin{tabular}{|c|c|} \hline Material & Specific Heat Capacity (\( J / kg \cdot °C \)) \\ \hline X & 380 \\ \hline Y & 910 \\ \hline Z & 470 \\ \hline \end{tabular} \][/tex]
Now, let's address each part of the question step-by-step:
### Part i:
Question: If the equal mass of [tex]\( X \)[/tex], [tex]\( Y \)[/tex], and [tex]\( Z \)[/tex] has the same temperature, which one has maximum heat?
Explanation:
- The heat energy ([tex]\( Q \)[/tex]) stored in a substance is given by the formula:
[tex]\[ Q = mc\Delta T \][/tex]
where:
- [tex]\( m \)[/tex] is the mass,
- [tex]\( c \)[/tex] is the specific heat capacity,
- [tex]\( \Delta T \)[/tex] is the temperature change.
- For equal mass ([tex]\( m \)[/tex]) and temperature ([tex]\( \Delta T \)[/tex]), the material with the highest specific heat capacity ([tex]\( c \)[/tex]) will store the maximum heat.
From the table:
- [tex]\( X \)[/tex]: [tex]\( 380 \, J/kg \cdot °C \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( 910 \, J/kg \cdot °C \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( 470 \, J/kg \cdot °C \)[/tex]
Among these, [tex]\( Y \)[/tex] has the highest specific heat capacity. Hence, the material [tex]\( Y \)[/tex] has the maximum heat at the same temperature and mass.
### Part ii:
Question: If three pieces of them have equal temperature and equal amount of heat, which one of them has maximum mass?
Explanation:
- Rearranging the heat energy formula:
[tex]\[ m = \frac{Q}{c\Delta T} \][/tex]
- For equal heat ([tex]\( Q \)[/tex]) and temperature change ([tex]\( \Delta T \)[/tex]), the material with the lowest specific heat capacity ([tex]\( c \)[/tex]) will have the highest mass ([tex]\( m \)[/tex]).
From the table:
- [tex]\( X \)[/tex]: [tex]\( 380 \, J/kg \cdot °C \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( 910 \, J/kg \cdot °C \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( 470 \, J/kg \cdot °C \)[/tex]
Among these, [tex]\( X \)[/tex] has the lowest specific heat capacity. Hence, the material [tex]\( X \)[/tex] will have the maximum mass for equal heat and temperature.
### Part iii:
Question: What do you mean by the specific heat capacity of [tex]\( Z \)[/tex] being [tex]\( 470 \, J/kg \cdot °C \)[/tex]?
Explanation:
- The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one kilogram of that substance by one degree Celsius.
For material [tex]\( Z \)[/tex]:
- A specific heat capacity of [tex]\( 470 \, J/kg \cdot °C \)[/tex] means that [tex]\( 470 \)[/tex] Joules of heat energy is required to raise the temperature of [tex]\( 1 \, kg \)[/tex] of material [tex]\( Z \)[/tex] by [tex]\( 1 \, °C \)[/tex].
### Part iv:
Question: If the equal mass having the same shape and size of them at [tex]\( 100 \, °C \)[/tex] temperature is kept over a wax slab, which of them will melt the wax to the maximum depth?
Explanation:
- When equal masses at the same temperature are kept over a wax slab, the one with the highest specific heat capacity will transfer the most heat to the wax, resulting in deeper melting.
From the table:
- [tex]\( X \)[/tex]: [tex]\( 380 \, J/kg \cdot °C \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( 910 \, J/kg \cdot °C \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( 470 \, J/kg \cdot °C \)[/tex]
Therefore, [tex]\( Y \)[/tex], having the highest specific heat capacity, will melt the wax to the maximum depth.
### Summary:
- i. Material [tex]\( Y \)[/tex] has the maximum heat.
- ii. Material [tex]\( X \)[/tex] has the maximum mass for equal heat and temperature.
- iii. The specific heat capacity of [tex]\( Z \)[/tex] being [tex]\( 470 \, J/kg \cdot °C \)[/tex] means that [tex]\( 470 \)[/tex] Joules of heat energy is required to raise the temperature of [tex]\( 1 \, kg \)[/tex] of material [tex]\( Z \)[/tex] by [tex]\( 1 \, °C \)[/tex].
- iv. Material [tex]\( Y \)[/tex] will melt the wax to the maximum depth.
### Given Table:
[tex]\[ \begin{tabular}{|c|c|} \hline Material & Specific Heat Capacity (\( J / kg \cdot °C \)) \\ \hline X & 380 \\ \hline Y & 910 \\ \hline Z & 470 \\ \hline \end{tabular} \][/tex]
Now, let's address each part of the question step-by-step:
### Part i:
Question: If the equal mass of [tex]\( X \)[/tex], [tex]\( Y \)[/tex], and [tex]\( Z \)[/tex] has the same temperature, which one has maximum heat?
Explanation:
- The heat energy ([tex]\( Q \)[/tex]) stored in a substance is given by the formula:
[tex]\[ Q = mc\Delta T \][/tex]
where:
- [tex]\( m \)[/tex] is the mass,
- [tex]\( c \)[/tex] is the specific heat capacity,
- [tex]\( \Delta T \)[/tex] is the temperature change.
- For equal mass ([tex]\( m \)[/tex]) and temperature ([tex]\( \Delta T \)[/tex]), the material with the highest specific heat capacity ([tex]\( c \)[/tex]) will store the maximum heat.
From the table:
- [tex]\( X \)[/tex]: [tex]\( 380 \, J/kg \cdot °C \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( 910 \, J/kg \cdot °C \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( 470 \, J/kg \cdot °C \)[/tex]
Among these, [tex]\( Y \)[/tex] has the highest specific heat capacity. Hence, the material [tex]\( Y \)[/tex] has the maximum heat at the same temperature and mass.
### Part ii:
Question: If three pieces of them have equal temperature and equal amount of heat, which one of them has maximum mass?
Explanation:
- Rearranging the heat energy formula:
[tex]\[ m = \frac{Q}{c\Delta T} \][/tex]
- For equal heat ([tex]\( Q \)[/tex]) and temperature change ([tex]\( \Delta T \)[/tex]), the material with the lowest specific heat capacity ([tex]\( c \)[/tex]) will have the highest mass ([tex]\( m \)[/tex]).
From the table:
- [tex]\( X \)[/tex]: [tex]\( 380 \, J/kg \cdot °C \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( 910 \, J/kg \cdot °C \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( 470 \, J/kg \cdot °C \)[/tex]
Among these, [tex]\( X \)[/tex] has the lowest specific heat capacity. Hence, the material [tex]\( X \)[/tex] will have the maximum mass for equal heat and temperature.
### Part iii:
Question: What do you mean by the specific heat capacity of [tex]\( Z \)[/tex] being [tex]\( 470 \, J/kg \cdot °C \)[/tex]?
Explanation:
- The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one kilogram of that substance by one degree Celsius.
For material [tex]\( Z \)[/tex]:
- A specific heat capacity of [tex]\( 470 \, J/kg \cdot °C \)[/tex] means that [tex]\( 470 \)[/tex] Joules of heat energy is required to raise the temperature of [tex]\( 1 \, kg \)[/tex] of material [tex]\( Z \)[/tex] by [tex]\( 1 \, °C \)[/tex].
### Part iv:
Question: If the equal mass having the same shape and size of them at [tex]\( 100 \, °C \)[/tex] temperature is kept over a wax slab, which of them will melt the wax to the maximum depth?
Explanation:
- When equal masses at the same temperature are kept over a wax slab, the one with the highest specific heat capacity will transfer the most heat to the wax, resulting in deeper melting.
From the table:
- [tex]\( X \)[/tex]: [tex]\( 380 \, J/kg \cdot °C \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( 910 \, J/kg \cdot °C \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( 470 \, J/kg \cdot °C \)[/tex]
Therefore, [tex]\( Y \)[/tex], having the highest specific heat capacity, will melt the wax to the maximum depth.
### Summary:
- i. Material [tex]\( Y \)[/tex] has the maximum heat.
- ii. Material [tex]\( X \)[/tex] has the maximum mass for equal heat and temperature.
- iii. The specific heat capacity of [tex]\( Z \)[/tex] being [tex]\( 470 \, J/kg \cdot °C \)[/tex] means that [tex]\( 470 \)[/tex] Joules of heat energy is required to raise the temperature of [tex]\( 1 \, kg \)[/tex] of material [tex]\( Z \)[/tex] by [tex]\( 1 \, °C \)[/tex].
- iv. Material [tex]\( Y \)[/tex] will melt the wax to the maximum depth.
