Chapter 1, Problem 40P

A chemistry student is performing in experiment to determine the temperature volume behaviour of a gas mixture at constant pressure and quantity. Due to technical difficulties, he could only obtain values at two temperatures as shown in the table below:

$\begin{array}{cc}T\left(°\text{C}\right)& V\left(L\right)\\ 50& 1.08\\ 98& 1.24\end{array}$ The student knows that the gas volume directly depends on temperature, that is, $V\left(T\right)=mT+K$, where V is the volume in L. T is the temperature in °C. K is the y -intercept in L, and in is the slope of the line in L/°C

(a) Find the equation of the line that describes the temperature volume relationship of the gas mixture, and determines the slope in of the linear relationship.

(b) Using the equation of the line from part (a), find the temperature of the gas mixture lithe volume is 1.15 L.

(c) Using the equation of the line from part (a), find the volume of the gas if the temperature is 70° C.

(d) Sketch the graph of the volume, temperature relationship for the gas mixture from -300°C to 100°C and clearly indicate both the slope m and the y -intercept. What k the significance of the temperature when $V=0\text{L}$ ?