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Chapter 3: Q9E (page 574)

An experimenter using a gas thermometer found the pressure at the triple point of water (0.01掳C) to be 4.80脳104Paand the pressure at the normal boiling point (100掳C) to be6.50脳104Pa. (a) Assuming that the pressure varies linearly with temperature, use these two data points to find the Celsius temperature at which the gas pressure would be zero (that is, find the Celsius temperature of absolute zero). (b) Does the gas in this thermometer obey Eq. (17.4) precisely? If that equation were precisely obeyed and the pressure at 100掳C were6.40脳104Pa, what pressure would the experimenter have measured at 0.01潞C?

Short Answer

Expert verified

(a) The Celsius temperature at which the gas pressure is zero is -282掳C.

(b) The pressure measured at 0.01潞C is 4.76脳104Pawhich suggests that the equation is not precisely followed.

Step by step solution

01

(a) Determination of Celsius temperature at which the gas pressure is zero.

The linear relation of pressure and temperature is,

p2=p1+yT2-T1

Solve for y,

y=p2-p1T2-T1

Substitute the values given to obtain the value of y,

y=6.50脳104Pa-4.80脳104Pa100掳C-0.01掳C=170.0Pa/C掳

Now for zero gas pressure, p=0. Thus, The temperature at the zero pressure of the gas is,

T=T1-p1y0.01掳C-4.80脳104Pa170.0Pa/C掳=-282掳C

02

(b) Determination of the pressure at the temperature 0.01ºC.

For this case,

T1=100掳C+273.15=373.15K and T2=0.01掳C+273.15=273.16K

Use equation, T2T1=P2P1, Here, T is in units of K in order to obtain the value of pressure.

localid="1664357082266" P2=P1T2T1P2=6.50脳104Pa273.16K373.15K=4.76脳104Pa

The measured pressure is 4.80脳104Paand the calculated pressure is 4.76脳104Pa. Therefore, the equation is not precisely followed.

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