21th-hmw-01

Each question carries 5 marks

Thermal Physics

Problem sheet 1
Due  28st September 2021

Reading Assignment 1 : First six sections of the class XII NCERT book, Chapter 12 ( Thermodynamics) Reading assignment 2: From the book Principles of Thermodynamics by N.D.Hari Dass CRC Press Section 1.1 ( discusses thermometry first six pages)

1. [1.] Show that constant volume thermometers using an ideal gas as well as a van der Waals gas both yield the same temperature scale when uniform scales are adopted. Equation of state for ideal gas is \(P V = nRT\) and for van der Wall gas is \begin{equation*} \Big(p + \frac{an^2}{V^2}\Big )(V − nb) = nRT \end{equation*}
2. [2.] A bimetallic strip of total thickness $x$ is straight at temperature $T$. What is the radius of curvature of the strip, $R$, when it is heated to temperature $T + ∆T$ ? The coefficients of linear expansion of the two metals are $α_1$ and $α_2$ , respectively, with \(α_1 > α_2 \). Assume each metal has thickness \(x/2\), and that \(x << R.\)
3. [3.] Which of the following quantities are extensive and which are intensive? (a) The magnetic moment of a gas. (b) The electric field \(E\) in a solid. (c) The length of a wire. (d) The surface tension of an oil film.