Chapter 13, Problem 1P

To determine

To Choose:The correct option.

Answer to Problem 1P

Option (e)

Explanation of Solution

Given:Gauge pressure is doubled.

Formula Used:

Gauge pressure:

  $P_{Gauge}=P_{Absolute}-P_{Atmospheric}$

Conclusion:

  $\begin{array}{l}{P}_{Gauge}=P_{Absolute}-P_{Atmospheric}\\ P_{Absolute}=P_{Gauge}+P_{Atmospheric}\end{array}$

The initial absolute pressure is given by

  $P_i=P+P_{atm}$

Where P is the initial gauge pressure.

The final absolute pressure is given by

  $P_f=2P+P_{atm}$

Now dividing the above equations:

  $\begin{array}{l}\frac{P_f}{P_i}=\frac{2P+P_{atm}}{P+P_{atm}}\\ \frac{P_f}{P_i}=1+\frac{P}{P+P_{atm}}\\ \frac{P}{P+P_{atm}}<1\\ \frac{P_f}{P_i}=1+\frac{P}{P+P_{atm}}\\ \frac{P_f}{P_i}<1+1=2\\ \frac{P_f}{P_i}<2\\ P_f<2P_i\end{array}$

Therefore, the final absolute pressure will be increased by a factor less than 2.