Answer :
Certainly! To tackle the problem effectively, let's break it down and answer each question systematically. Note that we will need additional information about the specific heats of substances X, Y, and Z to answer all questions correctly with absolute numerical values. However, we can provide a detailed general approach to each point.
### a. If all of them are liquids, which is suitable:
This part isn't clear since it is not related directly to the subsequent questions. We should elaborate on that assumption as the context.
### b. Study the given table and answer the following questions:
#### i. If the equal mass of X, Y and Z has the same temperature, which one has maximum heat?
The heat content (Q) of a substance is given by:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
where:
- \(m\) is the mass of the substance,
- \(c\) is the specific heat capacity,
- \(\Delta T\) is the change in temperature.
Since equal mass and temperature change (\(\Delta T\)) are considered, the substance with the highest specific heat capacity (c) will have the maximum heat content. Therefore, to find which one has maximum heat, compare the specific heat capacities of X, Y, and Z.
#### ii. If three pieces of them have equal temperature and equal amount of heat, which one of them has maximum mass?
Using the same heat capacity formula:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
Given that heat (\(Q\)) and temperature change (\(\Delta T\)) are the same, the mass (\(m\)) can be rearranged to:
[tex]\[ m = \frac{Q}{c \times \Delta T} \][/tex]
Thus, the substance with the lowest specific heat capacity \(c\) will have the maximum mass for the same heat content and temperature change.
#### iii. What do you mean by specific heat capacity of ' Z ' is \(470 \, J/(kg \cdot °C) \)?
The specific heat capacity of a substance is the amount of heat required to raise the temperature of one kilogram of the substance by one degree Celsius.
Therefore, a specific heat capacity of \(470 \, J/(kg \cdot °C)\) for substance Z means that \(470 \, \text{Joules}\) of heat energy is required to raise the temperature of \(1 \, \text{kg}\) of substance Z by \(1 \, \text{°C}\).
#### iv. If the equal mass having the same shape and size of them at \(100 \, \text{°C}\) temperature is kept over a wax slab, which of them will melt the wax for maximum depth?
The depth to which wax melts depends on the amount of heat transferred from the substance to the wax. Assuming that the equal mass and initial temperature are the same for each substance:
The substance that will provide the maximum heat energy to the wax is the one that has the highest specific heat capacity. The quantity of heat transferred (\(Q\)) is given by:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
Thus, the substance with the highest \(c\) (specific heat) will melt the wax more deeply because it can transfer more heat energy for the same change in conditions.
### Conclusion
- i. X, Y, or Z with the highest specific heat capacity will have maximum heat.
- ii. X, Y, or Z with the lowest specific heat capacity will have maximum mass.
- iii. The specific heat capacity of \(470 \, J/(kg \cdot °C)\) means 470 Joules is needed to raise 1 kg of Z by 1°C.
- iv. X, Y, or Z with the highest specific heat capacity will melt the wax the most.
Feel free to provide precise values for specific heat capacities to get exact answers.
### a. If all of them are liquids, which is suitable:
This part isn't clear since it is not related directly to the subsequent questions. We should elaborate on that assumption as the context.
### b. Study the given table and answer the following questions:
#### i. If the equal mass of X, Y and Z has the same temperature, which one has maximum heat?
The heat content (Q) of a substance is given by:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
where:
- \(m\) is the mass of the substance,
- \(c\) is the specific heat capacity,
- \(\Delta T\) is the change in temperature.
Since equal mass and temperature change (\(\Delta T\)) are considered, the substance with the highest specific heat capacity (c) will have the maximum heat content. Therefore, to find which one has maximum heat, compare the specific heat capacities of X, Y, and Z.
#### ii. If three pieces of them have equal temperature and equal amount of heat, which one of them has maximum mass?
Using the same heat capacity formula:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
Given that heat (\(Q\)) and temperature change (\(\Delta T\)) are the same, the mass (\(m\)) can be rearranged to:
[tex]\[ m = \frac{Q}{c \times \Delta T} \][/tex]
Thus, the substance with the lowest specific heat capacity \(c\) will have the maximum mass for the same heat content and temperature change.
#### iii. What do you mean by specific heat capacity of ' Z ' is \(470 \, J/(kg \cdot °C) \)?
The specific heat capacity of a substance is the amount of heat required to raise the temperature of one kilogram of the substance by one degree Celsius.
Therefore, a specific heat capacity of \(470 \, J/(kg \cdot °C)\) for substance Z means that \(470 \, \text{Joules}\) of heat energy is required to raise the temperature of \(1 \, \text{kg}\) of substance Z by \(1 \, \text{°C}\).
#### iv. If the equal mass having the same shape and size of them at \(100 \, \text{°C}\) temperature is kept over a wax slab, which of them will melt the wax for maximum depth?
The depth to which wax melts depends on the amount of heat transferred from the substance to the wax. Assuming that the equal mass and initial temperature are the same for each substance:
The substance that will provide the maximum heat energy to the wax is the one that has the highest specific heat capacity. The quantity of heat transferred (\(Q\)) is given by:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
Thus, the substance with the highest \(c\) (specific heat) will melt the wax more deeply because it can transfer more heat energy for the same change in conditions.
### Conclusion
- i. X, Y, or Z with the highest specific heat capacity will have maximum heat.
- ii. X, Y, or Z with the lowest specific heat capacity will have maximum mass.
- iii. The specific heat capacity of \(470 \, J/(kg \cdot °C)\) means 470 Joules is needed to raise 1 kg of Z by 1°C.
- iv. X, Y, or Z with the highest specific heat capacity will melt the wax the most.
Feel free to provide precise values for specific heat capacities to get exact answers.
