A Piston Contains 0.0884 Mol Of A Diatomic Gas. The Piston Is Compressed While 83.7 J Of Heat Are Removed. The Temperature Changes By − 18.8 ∘ C -18.8^{\circ} C − 18. 8 ∘ C .How Much Work Is Done By The Gas? W = [ ? ] J W=[?] \, J W = [ ?] J
Introduction
In thermodynamics, the work done by a gas is a crucial concept that helps us understand the energy transfer between the system and its surroundings. In this article, we will delve into the calculation of work done by a diatomic gas, which is a type of gas that consists of molecules with two atoms. We will use the given information about the piston, the amount of heat removed, and the temperature change to determine the work done by the gas.
The First Law of Thermodynamics
The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. Mathematically, this is expressed as:
ΔE = Q - W
where ΔE is the change in energy, Q is the heat added to the system, and W is the work done by the system.
Given Information
- The piston contains 0.0884 mol of a diatomic gas.
- 83.7 J of heat are removed from the piston.
- The temperature changes by .
Calculating the Change in Internal Energy
To calculate the work done by the gas, we need to first determine the change in internal energy (ΔE). We can use the formula:
ΔE = nCvΔT
where n is the number of moles, Cv is the specific heat capacity at constant volume, and ΔT is the change in temperature.
For a diatomic gas, the specific heat capacity at constant volume (Cv) is given by:
Cv = (5/2)R
where R is the gas constant.
Calculating the Change in Internal Energy (continued)
First, we need to convert the temperature change from Celsius to Kelvin:
ΔT = -18.8°C + 273.15 = -45.65 K
Next, we can calculate the change in internal energy:
ΔE = nCvΔT = 0.0884 mol × (5/2) × 8.314 J/mol·K × (-45.65 K) = -123.3 J
Calculating the Work Done by the Gas
Now that we have the change in internal energy, we can use the first law of thermodynamics to calculate the work done by the gas:
W = Q - ΔE
where Q is the heat removed from the piston.
Calculating the Work Done by the Gas (continued)
We are given that 83.7 J of heat are removed from the piston. Therefore, we can calculate the work done by the gas:
W = Q - ΔE = -83.7 J - (-123.3 J) = 39.6 J
Conclusion
In this article, we have calculated the work done by a diatomic gas using the given information about the piston, the amount of heat removed, and the temperature change. We have used the first law of thermodynamics and the specific heat capacity at constant volume to determine the change in internal energy and the work done by the gas. The result shows that the work done by the gas is 39.6 J.
References
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
Additional Resources
- Khan Academy: Thermodynamics
- MIT OpenCourseWare: Thermodynamics
- Physics Classroom: Thermodynamics
A Comprehensive Q&A Guide to Thermodynamics =====================================================
Introduction
In our previous article, we explored the concept of work done by a diatomic gas using the first law of thermodynamics. In this article, we will delve into a Q&A guide to thermodynamics, covering various topics and concepts related to thermodynamics. Whether you're a student, a teacher, or simply someone interested in learning more about thermodynamics, this guide is designed to provide you with a comprehensive understanding of the subject.
Q: What is thermodynamics?
A: Thermodynamics is the branch of physics that deals with the relationships between heat, work, and energy. It is a fundamental concept in physics that helps us understand how energy is transferred and transformed from one form to another.
Q: What are the three laws of thermodynamics?
A: The three laws of thermodynamics are:
- Zeroth Law of Thermodynamics: If two systems are in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.
- First Law of Thermodynamics: Energy cannot be created or destroyed, only converted from one form to another.
- Second Law of Thermodynamics: The total entropy of a closed system will always increase over time.
Q: What is entropy?
A: Entropy is a measure of the disorder or randomness of a system. It is a fundamental concept in thermodynamics that helps us understand how energy is transferred and transformed from one form to another.
Q: What is the difference between internal energy and enthalpy?
A: Internal energy (U) is the total energy of a system, including both kinetic energy and potential energy. Enthalpy (H) is the total energy of a system, including both internal energy and the energy associated with the pressure and volume of a system.
Q: What is the difference between heat and work?
A: Heat is the transfer of energy from one system to another due to a temperature difference. Work is the transfer of energy from one system to another through a force applied over a distance.
Q: What is the first law of thermodynamics in terms of heat and work?
A: The first law of thermodynamics can be expressed as:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Q: What is the second law of thermodynamics in terms of entropy?
A: The second law of thermodynamics can be expressed as:
ΔS = ΔQ / T
where ΔS is the change in entropy, ΔQ is the heat added to the system, and T is the temperature of the system.
Q: What is the difference between a reversible and irreversible process?
A: A reversible process is a process that can be reversed without any change in the system or its surroundings. An irreversible process is a process that cannot be reversed without any change in the system or its surroundings.
Q: What is the Carnot cycle?
A: The Carnot cycle is a theoretical cycle that is used to illustrate the second law of thermodynamics. It consists of four stages: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
Conclusion
In this Q&A guide to thermodynamics, we have covered various topics and concepts related to thermodynamics. Whether you're a student, a teacher, or simply someone interested in learning more about thermodynamics, this guide is designed to provide you with a comprehensive understanding of the subject.
References
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
- Feynman, R. P. (1963). The Feynman lectures on physics. Addison-Wesley.
Additional Resources
- Khan Academy: Thermodynamics
- MIT OpenCourseWare: Thermodynamics
- Physics Classroom: Thermodynamics