Physics question help PLEASE? Fluid pressure and temperature?

A person rides up a lift to a mountaintop, but the person’s ears fail to “pop” that is, the pressure of the inner ear does not equaliz with the outside atmosphere. The radius of each eardrum is 0.40 cm. The pressure of the atmosphere drops from 1.010 X 10^5 Pa at the bottom of the lift to 0.998 X 10^5 Pa at the top. What is the pressure on the inner ear at the top of the mountain? What is the magnitude of the net force on each eardrum?

1 Answer

  1. The pressure on the inner ear is 1.010×10^5 – .998×10^5 = 1200Pa outward

    So the net force = P*A = 1200Pa*π*(0.40×10^-2m)^2 = 0.0603N

Relevant information

Properties of Fluid: Pressure and Temperature!

The pressure is a force applied per unit area and is measured in units N/m2 or pascal.

The absolute pressure of a gas is the result of a large number of the molecules forming the gas striking the walls of the vessel. The force per unit area is called the specific pressure or just the pressure ‘P’. The unit of force is newton, N, and unit of area is 1 square metre, m2.

Thus the unit of pressure is one newton per square metre i.e. N/m2.

The standard SI unit of pressure is the pascal (Pa).

1 pascal = 1 N/m2.

Since this unit is very small, use is often made of a greater unit equal to 105 N/m2, called a bar, which does not belong to any system of units. The advantage claimed is that 1 bar is a pressure very nearly equal to the pressure of 1 standard atmosphere.

Distinction is made between absolute and gauge (excess) pressure. The absolute pressure Pabs is understood to mean the actual pressure of a working substance inside a vessel. The gauge pressure Pg shows the difference between the absolute pressure in a vessel and the pressure of the surroundings (atmospheric air). The absolute pressure may be higher or lower than the atmospheric pressure.

Pabs = Pg + Pa

Pabs = absolute pressure of the gas

Pg = gauge pressure

Pa = atmospheric pressure is measured in mm of water column. The head in centrifugal pump installations is measured in metres of water.

The principle of working for pressure gauges as well as vacuum gauges is the same. We commonly employ the Bourdon pressure gauge to measure the pressure of steam in a boiler, the pressure of lubricating oil in internal combustion engines and the pressure of air-steam mixture in a condenser.   

A manometer is employed to measure the slight variations in pressure of air and gas above or below atmosphere. Fig. 1-2 shows the working principle of a manometer. One limb of U-shaped glass tube is open to atmosphere and the other limb is connected to the gas supply or to the furnace. The liquid in the U-tube may be oil, water or mercury. The difference in heights of liquid columns gives the measurement of pressure.

Manometers and pressure gauges, generally, indicate pressure relative to the atmospheric pressure and in that case in order to determine the absolute pressure of the fluid we add the atmospheric pressure to the pressure gauge reading.

∴ Absolute pressure = Gauge pressure + Atmospheric pressure.

If b denotes the barometer reading in mm of mercury, then also absolute pressure bar = b / 750 + gauge reading (bar).

When the barometer reading is not known we assume that the atmospheric pressure is equal to one bar.

When the pressure of the fluid is less than the atmospheric pressure the gauge pressure becomes negative but it is frequently designated by a positive number and it is called vacuum. Vacuum is measured in mm of mercury column.

When we denote the pressures in bar, the gauge pressures will be expressed by a word “gauge”. If nothing is specified, we understand that the pressures are expressed in bar absolute.

Temperature is a quantitative measure of the degree of hotness or coldness of a system.

If two bodies or systems are in thermal equilibrium with a third body then all are in thermal equilibrium with each other, and hence they are at the same temperature. Refer fig. 1-3.

According to zeroth law of thermodynamics, a system is in thermal equilibrium if its temperature is uniform throughout and the same as the temperature of the surroundings. Thus, if two different bodies come to the same thermal equilibrium point with the same temperature sensing device, then the two bodies are at the same temperature.

The unit of temperature measurement is the degree. It is capable of determination provided two points can be obtained at which the intensity of heat is always constant. Generally freezing point of water and boiling point of water at an atmospheric pressure are selected for the purpose. If the distance between these two fixed points is divided into 100 equal divisions we get Centigrade scale or Celsius scale.

The fixed points on the Centigrade scale are:

Freezing point of water at atmospheric pressure – 0°C

Boiling point of water at atmospheric pressure – 100°C.

The 100 Celsius degrees is called the fundamental interval. The customary temperature scale adopted for use with the SI system of units is the Celsius scale.

The thermodynamic unit of temperature is the Kelvin (K). The present international definition of the Kelvin is that it is 1/273.16 of the thermodynamic temperature of the triple point of pure water.

Since the Celsius or Centigrade scale is only a part of the more extensive thermodynamic or absolute temperature scale, it is sometimes called a truncated thermodynamic scale.

Temperatures are measured by instruments known as:

(i) Thermometers.

(ii) Pyrometers.

There is no sharp distinction between these instruments but in general the pyrometer is ordinarily used for measuring higher temperatures.

In addition to the common form of thermometers, recording and resistance thermometers are extensively used.

The recording thermometer consists of a copper bulb connected to the instrument by a capillary copper tube which is protected by a heavy flexible bronze reinforcing tube. The capillary connects with a Bourdon spring coil form, located within the instrument and to which the pen is connected. Nitrogen gas is used in the bulb for temperature upto 550°C.

As temperature changes, the volume of gas increases or decreases thus moving the pen across the chart exactly in proportion to the temperature, change. Since the coefficient of expansion for nitrogen is uniform the chart is evenly graduated.

The resistance thermometer (fig. 1-4) consists of a nickel or platinum resistance enclosed in a protecting bulb. The operation depends upon the principle that the change in the resistance of the wire of resistance coil in the bulb is proportional to the change in the temperature of the bulb.

In using the instrument the variable resistance is adjusted to get null reading in galvanometer. The readings of R4 are calibrated to read temperatures. The compensating leads which are identical to the leads to the platinum resistance coil are inserted in the sheath.

They are connected to the arm of the bridge containing R4. This is to balance the resistance of the leads to the resistance coil at any temperature. Therefore the value of R4 is directly proportional to increase in coil resistance due to temperature.

Besides the Centigrade scale there is another scale, which is used in calculation work in engineering problems, known as Absolute Temperature Scale. This scale is based on so called Absolute Zero of temperature or the point at which a perfect gas is considered to have a zero volume.

It has been found that a perfect gas expands or contracts 1/273 of its volume at zero degree C for each degree centigrade change in temperature when pressure remains constant. Therefore, the absolute zero may be taken as 273°C below the melting point of ice. The absolute temperature in Centigrade scale is called degree Kelvin.

The relation between the various scales of temperature is as follows:

Temperature K = Temperature °C + 273.15 (can use 273 for most calculations).

The absolute thermodynamic temperature scale is called the Kelvin scale as this scale was devised by Lord Kelvin in about 1851. A temperature T on the Kelvin scale is written T K and not T °K.

The Kelvin degree has the same magnitude as the Celsius degree for all practical purposes.

The NTP and STP both refer to standard atmospheric pressure of 760 mm of mercury. In calorimetry and similar work the tests are carried out at the usual laboratory temperature and the results adjusted to 15°C, this temperature being recognised as standard for this purpose.

Thus, for gas calculation NTP means 760 mm of mercury pressure and 0°C, and STP means 760 mm of mercury pressure and 15°C. Sometimes we use the term normal volume of a gas. The volume occupied by a gas at NTP is known as the normal volume. The volume of a gas changes with pressure and temperature. By introducing the term normal volume we can compare the different gases.

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