Important Heat And Thermodynamics Formulas For JEE
The field of thermodynamics and the study of heat are central pillars in the realm of physics and play a significant role in the Joint Entrance Examination (JEE). To excel in this competitive exam, it's crucial to have a solid grasp of the essential heat and thermodynamics formulas. In this article, we will unravel these critical formulas, discuss their importance, and explore how they are applied in solving complex problems in the JEE examination.
First Law of Thermodynamics (Law of Energy Conservation)
The first law of thermodynamics is a fundamental principle that states that energy cannot be created or destroyed; it can only change forms. In mathematical terms, it can be expressed as:
ΔU=Q−W
Where:
- ΔU represents the change in internal energy of a system.
- Q denotes the heat added to the system.
- W stands for the work done by the system.
Understanding this formula is pivotal in analyzing energy transformations within thermodynamic systems.
Second Law of Thermodynamics (Clausius Statement)
The second law of thermodynamics deals with the direction of heat flow and the concept of entropy. It is often summarized as "heat flows spontaneously from a hotter body to a colder one." In thermodynamics, it's represented by various mathematical expressions and inequalities, such as:
ΔS≥Q/T
This law helps in understanding the irreversibility of certain processes and is crucial for solving thermodynamics problems in JEE.
Work Done by an Ideal Gas
The work done by an ideal gas during a process can be calculated using the formula:
W=PΔV
Where:
- W is the work done.
- P is the pressure.
- ΔV is the change in volume.
This formula is instrumental in analyzing various thermodynamic processes.
Heat Transfer (Fourier's Law)
The rate of heat transfer through a material is given by Fourier's Law:
Q=−kA ΔT/d
- Where:
- Q is the rate of heat transfer.
- k is the thermal conductivity of the material.
- A is the cross-sectional area.
- ΔT is the temperature difference.
- d is the thickness of the material.
This formula is essential for understanding heat conduction and solving related problems.
Thermal Emissions (Wien's Displacement Law)
The wavelength of maximum emission (λ max) is inversely proportional to the absolute temperature (T). λ max T=b, where λ Max represents the peak wavelength of a blackbody radiation curve,
b is the Wien's constant (0.282 cm-K), and T is the temperature.
Stefan-Boltzmann Law
For a perfect blackbody, the energy flux (u/A) is given by u=σAT4
Here, σ is the Stefan-Boltzmann constant (5.6x10−8 5.67x10−8watt/m²K⁴).
In the case of a non-perfect blackbody, the energy flux (u) is modified to u=eσAT4, where e represents emissivity (absorptive power) ranging between 0 and 1.
Heat and thermodynamics are fundamental topics in physics and are integral to the JEE syllabus. A strong command of these essential formulas is not only essential for excelling in the JEE examination but also for comprehending the behavior of energy and matter in the physical world. By mastering these formulas and their applications, you'll be well-equipped to tackle thermodynamics questions in your JEE exam and develop a deeper appreciation for the fascinating world of heat and energy transformations
Important Heat And Thermodynamics Formulas For JEE FAQs
Q1. What is the First Law of Thermodynamics, and how is it represented?
Ans. The First Law states that ΔU (change in internal energy) equals Q (heat added) minus W (work done).
Q2. Explain the Second Law of Thermodynamics in simple terms.
Ans. Heat spontaneously flows from hotter to colder bodies.
Q3. What's the formula for work done by an ideal gas?
Ans. W=PΔV.
Q4. How can you calculate the rate of heat transfer through a material?
Ans. Use Fourier's Law:
- Q=−kA ΔT/d
Q5. What does Wien's Displacement Law express, and what is the formula?
Ans. It relates the peak wavelength (λ max) of thermal radiation to temperature (T): λ max T=b, where b is Wien's constant.
