What Is The Specific Heat Of A Substance If A Mass Of 10.0 Kg Increases In Temperature From $10.0^{\circ} C$ To $70.0^{\circ} C$ When 2,520 J Of Heat Is Applied?Use The Formula $q = M C_p \Delta T$.A. $0.00420 \,
Introduction
In thermodynamics, the specific heat of a substance is a measure of the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or Kelvin). This property is crucial in understanding various physical and chemical processes, such as heat transfer, phase transitions, and chemical reactions. In this article, we will explore the concept of specific heat and use a practical example to calculate the specific heat of a substance.
What is Specific Heat?
Specific heat is defined as the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). It is denoted by the symbol C_p and is typically expressed in units of joules per kilogram per degree Celsius (J/kg°C). The specific heat of a substance depends on its physical and chemical properties, such as its molecular structure, density, and thermal conductivity.
The Formula for Specific Heat
The formula for specific heat is given by:
q = m C_p ΔT
where:
qis the amount of heat energy applied to the substance (in joules, J)mis the mass of the substance (in kilograms, kg)C_pis the specific heat of the substance (in J/kg°C)ΔTis the change in temperature (in degrees Celsius, °C)
Calculating Specific Heat
Let's use the given example to calculate the specific heat of a substance. We are given:
- Mass of the substance:
m = 10.0 kg - Initial temperature:
T_initial = 10.0°C - Final temperature:
T_final = 70.0°C - Amount of heat energy applied:
q = 2,520 J
We need to calculate the specific heat C_p using the formula:
q = m C_p ΔT
First, we need to calculate the change in temperature ΔT:
ΔT = T_final - T_initial = 70.0°C - 10.0°C = 60.0°C
Now, we can plug in the values into the formula:
2,520 J = 10.0 kg C_p (60.0°C)
To solve for C_p, we can divide both sides by m ΔT:
C_p = 2,520 J / (10.0 kg × 60.0°C)
C_p = 2,520 J / 600 kg°C
C_p = 0.00420 J/kg°C
Conclusion
In this article, we have explored the concept of specific heat and used a practical example to calculate the specific heat of a substance. We have shown that the specific heat of a substance can be calculated using the formula q = m C_p ΔT, where q is the amount of heat energy applied, m is the mass of the substance, C_p is the specific heat of the substance, and ΔT is the change in temperature. We have also calculated the specific heat of a substance using the given example and obtained a value of 0.00420 J/kg°C.
Discussion
The specific heat of a substance is an important property that can be used to understand various physical and chemical processes. It is a measure of the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or Kelvin). The specific heat of a substance depends on its physical and chemical properties, such as its molecular structure, density, and thermal conductivity.
In conclusion, the specific heat of a substance is a crucial property that can be used to understand various physical and chemical processes. It is a measure of the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or Kelvin). We have shown that the specific heat of a substance can be calculated using the formula q = m C_p ΔT, where q is the amount of heat energy applied, m is the mass of the substance, C_p is the specific heat of the substance, and ΔT is the change in temperature.
References
- [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics (9th ed.). John Wiley & Sons.
- [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers (10th ed.). Cengage Learning.
Appendix
The following is a list of common specific heat values for various substances:
| Substance | Specific Heat (J/kg°C) |
|---|---|
| Water | 4.184 |
| Air | 1.005 |
| Copper | 0.385 |
| Aluminum | 0.904 |
| Steel | 0.502 |
Q: What is specific heat?
A: Specific heat is a measure of the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). It is denoted by the symbol C_p and is typically expressed in units of joules per kilogram per degree Celsius (J/kg°C).
Q: Why is specific heat important?
A: Specific heat is an important property that can be used to understand various physical and chemical processes, such as heat transfer, phase transitions, and chemical reactions. It is also used in the design of heating and cooling systems, as well as in the development of materials with specific thermal properties.
Q: How is specific heat calculated?
A: The specific heat of a substance can be calculated using the formula q = m C_p ΔT, where q is the amount of heat energy applied, m is the mass of the substance, C_p is the specific heat of the substance, and ΔT is the change in temperature.
Q: What are some common specific heat values?
A: Some common specific heat values for various substances are:
| Substance | Specific Heat (J/kg°C) |
|---|---|
| Water | 4.184 |
| Air | 1.005 |
| Copper | 0.385 |
| Aluminum | 0.904 |
| Steel | 0.502 |
Q: How does temperature affect specific heat?
A: The specific heat of a substance can vary with temperature. In general, the specific heat of a substance increases with temperature, but the relationship between specific heat and temperature is not always linear.
Q: Can specific heat be measured experimentally?
A: Yes, specific heat can be measured experimentally using a variety of techniques, including calorimetry and thermometry.
Q: What are some applications of specific heat?
A: Specific heat has a wide range of applications, including:
- Design of heating and cooling systems
- Development of materials with specific thermal properties
- Understanding of phase transitions and chemical reactions
- Analysis of heat transfer processes
Q: Can specific heat be used to predict the behavior of a substance under different conditions?
A: Yes, specific heat can be used to predict the behavior of a substance under different conditions, such as changes in temperature, pressure, or composition.
Q: What are some common mistakes to avoid when working with specific heat?
A: Some common mistakes to avoid when working with specific heat include:
- Failing to account for the temperature dependence of specific heat
- Using incorrect values for specific heat
- Failing to consider the effects of phase transitions and chemical reactions on specific heat
Q: How can specific heat be used to improve the efficiency of a system?
A: Specific heat can be used to improve the efficiency of a system by optimizing the design of heating and cooling systems, selecting materials with specific thermal properties, and understanding the behavior of substances under different conditions.
Q: Can specific heat be used to predict the behavior of a substance under different environmental conditions?
A: Yes, specific heat can be used to predict the behavior of a substance under different environmental conditions, such as changes in temperature, pressure, or composition.
Q: What are some future directions for research in specific heat?
A: Some future directions for research in specific heat include:
- Development of new materials with specific thermal properties
- Investigation of the effects of phase transitions and chemical reactions on specific heat
- Development of new experimental techniques for measuring specific heat
- Application of specific heat to new fields, such as energy storage and conversion.