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Chapter 6: Problem 7

At times, a pressure is stated in units of mass per unit area rather than force per unit area. Express \(P=1 \mathrm{atm}\) in the unit \(\mathrm{kg} / \mathrm{cm}^{2}\) [Hint: How is a mass in kilograms related to a force?]

Short Answer

Expert verified
1 atm is approximately equivalent to \(1.03 \, \mathrm{kg/cm^{2}}\).

Step by step solution

01

Understand the relationship between force and mass

Force is defined as mass times acceleration. In this case, the mass is in kilograms and the acceleration is the gravitational acceleration, which is approximately \(9.8 \, \mathrm{m/s^{2}}\) on the Earth's surface. Therefore, a mass \(m\) in kilograms exerts a force of \(m \times 9.8 \, \mathrm{N}\).
02

Convert 1 atm to Newton per square meter (Pascal)

1 atm is equivalent to \(101325 \, \mathrm{Pa}\) or \(101325 \, \mathrm{N/m^{2}}\). This means that 1 atm exerts a force of \(101325 \, \mathrm{N}\) on each square meter.
03

Convert Newtons to kilograms-force

Now we can use the relationship between mass and force to convert from Newtons to kg-force. We use the approximate value for the acceleration due to gravity, so \(1 \, \mathrm{N} = 1/9.8 \, \mathrm{kgf}\). Thus, \(101325 \, \mathrm{N} = 101325/9.8 \, \mathrm{kgf} \approx 10332.65 \, \mathrm{kgf/m^{2}}\).
04

Convert from square meter to square centimeter

We need to convert the area from square meters to square centimeters. We know that \(1 \, \mathrm{m^{2}} = 10000 \, \mathrm{cm^{2}}\), so \(10332.65 \, \mathrm{kgf/m^{2}} = 10332.65 / 10000 \, \mathrm{kgf/cm^{2}} = 1.033 \, \mathrm{kgf/cm^{2}}\) which is approximately equal to \(1.03 \, \mathrm{kg/cm^{2}}\).
05

Final answer

So to convert 1 atm into the unit of kg/cm², we get 1 atm = \(1.03 \, \mathrm{kg/cm^{2}}\).

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Most popular questions from this chapter

The equation \(d / P=M / R T,\) which can be derived from equation \((6.14),\) suggests that the ratio of the density \((d)\) to pressure (P) of a gas at constant temperature should be a constant. The gas density data at the end of this question were obtained for \(\mathrm{O}_{2}(\mathrm{g})\) at various pressures at \(273.15 \mathrm{K}\) (a) Calculate values of \(d / P,\) and with a graph or by other means determine the ideal value of the term \(d / P\) for \(\mathrm{O}_{2}(\mathrm{g})\) at \(273.15 \mathrm{K}\) [Hint: The ideal value is that associated with a perfect (ideal) gas.] (b) Use the value of \(d / P\) from part (a) to calculate a precise value for the atomic mass of oxygen, and compare this value with that listed on the inside front cover. $$\begin{array}{lllll} P, \mathrm{mmHg}: & 760.00 & 570.00 & 380.00 & 190.00 \\ d, \mathrm{g} / \mathrm{L}: & 1.428962 & 1.071485 & 0.714154 & 0.356985 \end{array}$$

Explain why the height of the mercury column in a barometer is independent of the diameter of the barometer tube.

In the reaction of \(\mathrm{CO}_{2}(\mathrm{g})\) and solid sodium peroxide \(\left(\mathrm{Na}_{2} \mathrm{O}_{2}\right),\) solid sodium carbonate \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right)\) and oxy- gen gas are formed. This reaction is used in submarines and space vehicles to remove expired \(\mathrm{CO}_{2}(\mathrm{g})\) and to generate some of the \(\mathrm{O}_{2}(\mathrm{g})\) required for breathing. Assume that the volume of gases exchanged in the lungs equals \(4.0 \mathrm{L} / \mathrm{min},\) the \(\mathrm{CO}_{2}\) content of expired air is \(3.8 \% \mathrm{CO}_{2}\) by volume, and the gases are at \(25^{\circ} \mathrm{C}\) and \(735 \mathrm{mmHg}\). If the \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) in the above reaction are measured at the same temperature and pressure, (a) how many milliliters of \(\mathrm{O}_{2}(\mathrm{g})\) are produced per minute and \((\mathrm{b})\) at what rate is the \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) consumed, in grams per hour?

Determine \(u_{\mathrm{m}}, \bar{u},\) and \(u_{\mathrm{rms}}\) for a group of ten automobiles clocked by radar at speeds of 38,44,45,48,50 \(55,55,57,58,\) and \(60 \mathrm{mi} / \mathrm{h},\) respectively.

What is the molar volume of an ideal gas at (a) \(25^{\circ} \mathrm{C}\) and 1.00 atm; \((b) 100^{\circ} \mathrm{C}\) and 748 Torr?
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