Reciprocal refers to the inverse of a number or quantity. For a number x its reciprocal is 1/x. In mathematics the reciprocal of a fraction a/b is b/a. The concept is widely used in algebra calculus and various fields like physics and engineering to simplify equations and calculations.
Class 11 Physics Chapter 10 Thermal Properties of Matter deals with concepts like temperature heat and thermal expansion. It explains the behavior of solids liquids and gases under temperature changes. The chapter also covers heat transfer methods specific heat capacity and the laws governing thermal expansion and specific phenomena such as absolute zero and heat engines.
We know that for an ideal gas at constant pressure, the volume is given by
V = nRT
where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature.
Now, for a small change in temperature, the change in volume can be written as:
dV = βV dT
where β is the coefficient of cubical expansion and dT is the change in temperature.
From the equation of state, V = nRT, we have:
dV = nR dT
Comparing the two expressions for dV, we get:
βV = nR / V
Since V = nRT, we can substitute this into the above equation:
β = 1 / T
Therefore, the coefficient of cubical expansion β for an ideal gas at constant pressure is equal to the reciprocal of its absolute temperature.
See more:
https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/