The ratio of specific heats
\((\frac{c_p}{c_v}) \)
in terms of degree of freedom (f) is given by:
The ratio of specific heats
\((\frac{c_p}{c_v}) \)
in terms of degree of freedom (f) is given by:
- \((1+\frac{f}{3})\)
- \((1+\frac{2}{f})\)
- \((1+\frac{f}{2})\)
- \((1+\frac{1}{f})\)
The Correct Option is A
Solution and Explanation
The correct option is(B): \((1+\frac{1}{f})\).
\(\frac{c_p}{c_v}=γ\)
\(c_v=(\frac{f}{2})R\)
and
\(C_p-C_v=R\)
\(⇒\frac{c_p}{c}=\frac{1+\frac{f}{2}}{\frac{f}{2}}\)
\(1+\frac{2}{f}\)
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Concepts Used:
Temperature Dependence of Resistance
The temperature dependence of resistance is a fundamental property of all materials that conduct electricity. Generally, the resistance of a conductor increases with an increase in temperature. This phenomenon is known as a positive temperature coefficient of resistance.
The reason for this temperature dependence of resistance is related to the interaction of electrons with the crystal lattice of the material. At lower temperatures, the lattice vibrations are minimal, and the electrons are free to move through the material with minimal scattering. This results in a low resistance to the flow of current. However, as the temperature increases, the lattice vibrations increase, causing the electrons to scatter more frequently, which increases resistance.
This phenomenon is governed by the relationship between resistance and temperature known as the temperature coefficient of resistance. The temperature coefficient of resistance is defined as the rate at which resistance changes with respect to temperature. The temperature coefficient of resistance is positive for most metals and semiconductors, meaning that resistance increases with increasing temperature.
However, there are a few materials, such as carbon and certain semiconductors, which exhibit a negative temperature coefficient of resistance. In these materials, the resistance decreases as the temperature increases.
The temperature dependence of resistance has important practical implications in the design and operation of electrical circuits and devices. For example, it is essential to consider the effect of temperature on the resistance of electronic components to ensure reliable and efficient operation of devices over a range of temperatures.
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