The following table shows the relationship between pressure (in atmospheres) and volume (in liters) of hydrogen gas at 0 °C. $$\begin{array} { | l | c | c | c | c | c | c | }
\hline \text { Pressure (atm) } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Volume (L) } & 22.4 & 11.2 & 7.5 & 5.6 & 4.5 & 3.7 \
\hline
\end{array}$$ (a) Find the average rate of change of volume with respect to pressure for the following pressure intervals:
(i) [1, 3]
(ii) [2, 3]
(iii) [4, 5]
(b) Plot the data points and fit an appropriate power function to these data.(c) Use the model from part (b) and determine the instantaneous rate of change of volume with respect to pressure.(d) Compare the instantaneous rate at P = 5 with the average rate for [4, 5]. Which is larger? Why is this the case?

Question

The following table shows the relationship between pressure (in atmospheres) and volume (in liters) of hydrogen gas at 0 °C. $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Pressure (atm) } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Volume (L) } & 22.4 & 11.2 & 7.5 & 5.6 & 4.5 & 3.7 \
\hline
\end{array}$$ (a) Find the average rate of change of volume with respect to pressure for the following pressure intervals:
(i) [1, 3]
(ii) [2, 3]
(iii) [4, 5]
(b) Plot the data points and fit an appropriate power function to these data.(c) Use the model from part (b) and determine the instantaneous rate of change of volume with respect to pressure.(d) Compare the instantaneous rate at P = 5 with the average rate for [4, 5]. Which is larger? Why is this the case?

Quizplus · Accepted Answer

The Answer of The following table shows the relationship between pressure (in atmospheres) and volume (in liters) of hydrogen gas at 0 °C. $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Pressure (atm) } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Volume (L) } & 22.4 & 11.2 & 7.5 & 5.6 & 4.5 & 3.7 \
\hline
\end{array}$$ (a) Find the average rate of change of volume with respect to pressure for the following pressure intervals:
(i) [1, 3]
(ii) [2, 3]
(iii) [4, 5]
(b) Plot the data points and fit an appropriate power function to these data.(c) Use the model from part (b) and determine the instantaneous rate of change of volume with respect to pressure.(d) Compare the instantaneous rate at P = 5 with the average rate for [4, 5]. Which is larger? Why is this the case?

The Following Table Shows the Relationship Between Pressure (In Atmospheres)