   Chapter 10, Problem 6P

Chapter
Section
Textbook Problem

In a student experiment, a constant-volume gas thermometer is calibrated in dry ice (−78.5°C) and in boiling ethyl alcohol (78.0°C). The separate pressures are 0.900 atm and 1.635 atm. (a) What value of absolute zero in degrees Celsius does the calibration yield? What pressures would be found at (b) the freezing and (c) boiling points of water? Hint: Use the linear relationship P = A + BT, where A and B are constants.

(a)

To determine
The value of absolute zero in Celsius.

Explanation

Section 1:

Explanation:

To determine: The constants a and b.

The constant (a) is 4.7×103atm/οC

The constant (b) is 1.27 atm.

Given Info: The pressure ( P1 ) is 0.900 atm when temperature ( T1 ) is 78.5οC . The pressure ( P2 ) is 1.635 atm when temperature ( T2 ) is 78.0οC .

Since, the volume is constant, the P-T graph is a straight line of the form,

P=aT+b                            (I)

• P is the pressure.
• T is the temperature.
• a and b are constants.

For the two sets of pressure and temperature,

P1=aT1+b                           (II)

P2=aT2+b                         (III)

From Equations (I) and (II),

a=P1P2T1T2                         (IV)

Substitute 0.900 atm for P1 , 78.5οC for T1 , 1.635 atm for P2 and 78.0οC for T2 to get a.

a=(0.900atm)(1.635atm)[78.5οC][78

(b)

To determine
The pressure.

(c)

To determine
The pressure.

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