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YF_ISM_17 - TEMPERATURE AND HEAT 17 17.1 IDENTIFY and SET...

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17-1 T EMPERATURE AND H EAT 17.1. I DENTIFY and S ET U P : 9 F C 5 32 T T = + °. E XECUTE : (a) F (9/5)( 62.8) 32 81.0 F T = + = ° (b) F (9/5)(56.7) 32 134.1 F T = + = ° (c) F (9/5)(31.1) 32 88.0 F T = + = ° E VALUATE : Fahrenheit degrees are smaller than Celsius degrees, so it takes more F° than C° to express the difference of a temperature from the ice point. 17.2. I DENTIFY and S ET U P : 5 C F 9 ( 32 ) T T = ° E XECUTE : (a) C (5/9)(41.0 32) 5.0 C T = = ° (b) C (5/9)(107 32) 41.7 C T = = ° (c) C (5/9)( 18 32) 27.8 C T = = ° E VALUATE : Fahrenheit degrees are smaller than Celsius degrees, so it takes more F° than C° to express the difference of a temperature from the ice point. 17.3. I DENTIFY : Convert each temperature from °C to °F. S ET U P : 9 F C 5 32 C T T = + ° E XECUTE : 18 C ° equals 9 5 (18 ) 32 64 F + = ° ° ° and 39 C ° equals 9 5 (39 ) 32 102 F. + = ° ° ° The temperature increase is 102 F 64 F 38 F = ° ° °. E VALUATE : The temperature increase is 21 C°, and this corresponds to 9 5 F (21 C ) 38 F 1 C = ° ° °. ° 17.4. I DENTIFY : Convert 10 K T Δ = to F °. S ET U P : 9 5 1 K 1 C F . = ° = ° E XECUTE : A temperature increase of 10 K corresponds to an increase of 18 F°. Beaker B has the higher temperature. E VALUATE : Kelvin and Celsius degrees are the same size. Fahrenheit degrees are smaller, so it takes more of them to express a given T Δ value. 17.5. I DENTIFY : Convert T Δ in kelvins to C° and to F°. S ET U P : 9 5 1 K 1 C F = = ° ° E XECUTE : (a) ( ) 9 9 F C 5 5 10.0 C 18.0 F T T Δ = Δ = ° = ° (b) C K 10.0 C T T Δ = Δ = ° E VALUATE : Kelvin and Celsius degrees are the same size. Fahrenheit degrees are smaller, so it takes more of them to express a given T Δ value. 17.6. I DENTIFY : Convert T Δ between different scales. S ET U P : T Δ is the same on the Celsius and Kelvin scales. 180 F 100 C = ° °, so 9 5 1 C F = ° °. E XECUTE : (a) 49.0 F T Δ = °. 9 5 1 C (49.0 F ) 27.2 C F T Δ = = ° ° °. ° (b) 100 F T Δ = °. 9 5 1 C ( 100.0 F ) 55.6 C F T Δ = = ° ° ° ° E VALUATE : The magnitude of the temperature change is larger in F° than in C°. 17
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17-2 Chapter 17 17.7. I DENTIFY : Convert T in °C to °F. S ET U P : 9 F C 5 ( 32 ) T T = + ° E XECUTE : (a) 9 F 5 (40.2 ) 32 104.4 F. T = + = ° ° ° Yes, you should be concerned. (b) 9 9 F C 5 5 ( 32 ) (12 C) 32 54 F. T T = + = + = ° ° ° ° E VALUATE : In doing the temperature conversion we account for both the size of the degrees and the different zero points on the two temperature scales. 17.8. I DENTIFY : Set C F T T = and F K . T T = S ET U P : 9 F C 5 32 C T T = + ° and 5 K C F 9 273.15 ( 32 ) 273.15 T T T = + = + ° E XECUTE : (a) F C T T T = = gives 9 5 32 T T = + ° and 40 ; T = ° 40 C 40 F. = ° ° (b) F K T T T = = gives 5 9 ( 32 ) 273.15 T T = + ° and ( ) ( ) 9 5 4 9 (32 ) 273.15 575 ; T = + = ° ° 575 F 575 K. = ° E VALUATE : Since K C 273.15 T T = + there is no temperature at which Celsius and Kelvin thermometers agree. 17.9. I DENTIFY : Convert to the Celsius scale and then to the Kelvin scale. S ET U P : Combining Eq.(17.2) and Eq.(17.3), ( ) 5 K F 9 32 273.15, T T = ° + E XECUTE : Substitution of the given Fahrenheit temperatures gives (a) 216.5 K (b) 325.9 K (c) 205.4 K E VALUATE : All temperatures on the Kelvin scale are positive.
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