Chapter 1, Problem 1.34E

Interpretation Introduction

Interpretation:

A derivative with respect to the same variable can be taken more than once:

$\frac{\delta }{\delta x}\left(\frac{\delta F}{\delta x}\right)=\frac{{\delta }^{2}F}{\delta F^2}$

and is called the second derivative of F. The following expressions are to be evaluated, assuming the ideal gas law applies.

$\begin{array}{l}(\text{a}){\left(\frac{{\delta }^{2}V}{\delta p^2}\right)}_{n,T}\\ (b){\left(\frac{{\delta }^{2}p}{\delta T^2}\right)}_{n,V}\end{array}$

Concept introduction:

Slope of a line is defined as both direction and the steepness of the line. The value of slope is denoted by the letter ‘m’. In a straight-line equation y = mx + c, the slope is ‘m’. Generally, the slope of a line is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points. The ideal gas law or general gas equation is the equation of state of a hypothetical ideal gas. The term was first coined by Emile Clapeyron in the year of 1834 as combination of other laws. The ideal gas law can be written as PV = nRT.