Chapter 10, Problem 2P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# The pressure in a constant-volume gas thermometer is 0.700 atm at 1.00 × 102°C and 0.512 atm at 0°C. (a) What is the temperature when the pressure is 0.040 0 atm? (b) What is the pressure at 450°C?

(a)

To determine
The temperature.

Explanation

Section 1:

Explanation:

To determine: The constants a and b.

The constant (a) is 1.88Ã—10âˆ’3â€‰atm/Î¿C

The constant (b) is 0.512 atm.

Given Info: The pressure ( P1 ) is 0.700 atm when temperature ( T1 ) is (1.00Ã—102)Î¿C . The pressure ( P2 ) is 0.512 atm when temperature ( T2 ) is 0Î¿C .

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

P=aT+b Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (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 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (II)

P2=aT2+b Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (III)

From Equations (I) and (II),

a=P1âˆ’P2T1âˆ’T2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (IV)

Substitute 0.700 atm for P1 , (1.00Ã—102)Î¿C for T1 , 0.512 atm for P2 and 0Î¿C for T2 to get a.

a=(0.700â€‰atm)âˆ’(0.512â€‰atm)[(1

(b)

To determine
The pressure.

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