The following equation can be used to relate the density of Equid water to Celsius temperature in the range from 0 °C to about 20 °C: d ( g / c m 3 ) = 0.99984 + ( 1.6945 × 10 − 2 t ) − ( 7.987 × 10 − 6 t 2 ) 1 + ( 1.6880 + 10 − 2 t ) a. To four significant figures, determine the density of water at 10 °C. b. At what temperature does water have a density of 0.99860 g/cm 3 ? c. In the following ways, show that the density passes through a maximum somewhere in the temperature range to which the equation applies. i. by estimation ii. by a graphical method iii. by a method based on differential calculus
The following equation can be used to relate the density of Equid water to Celsius temperature in the range from 0 °C to about 20 °C: d ( g / c m 3 ) = 0.99984 + ( 1.6945 × 10 − 2 t ) − ( 7.987 × 10 − 6 t 2 ) 1 + ( 1.6880 + 10 − 2 t ) a. To four significant figures, determine the density of water at 10 °C. b. At what temperature does water have a density of 0.99860 g/cm 3 ? c. In the following ways, show that the density passes through a maximum somewhere in the temperature range to which the equation applies. i. by estimation ii. by a graphical method iii. by a method based on differential calculus
Solution Summary: The author explains how the density of water is calculated using the following formula: d= mV Here, m is mass and V is volume.
The following equation can be used to relate the density of Equid water to Celsius temperature in the range from 0 °C to about 20 °C:
d
(
g
/
c
m
3
)
=
0.99984
+
(
1.6945
×
10
−
2
t
)
−
(
7.987
×
10
−
6
t
2
)
1
+
(
1.6880
+
10
−
2
t
)
a. To four significant figures, determine the density of water at 10 °C. b. At what temperature does water have a density of 0.99860 g/cm3? c. In the following ways, show that the density passes through a maximum somewhere in the temperature range to which the equation applies. i. by estimation ii. by a graphical method iii. by a method based on differential calculus
Boyle’s law for confined gases states that if the temperature is constant, pv = c, where p ispressure, v is volume, and c is a constant. At a certain instant the volume is 75 cubic inches, thepressure is 30 psi, and the pressure is decreasing at the rate of 2 psi every minute. What is therate of change of the volume at that instant?
(a) Amonton’s law expresses the relationship between pressureand temperature. Use Charles’s law and Boyle’s law toderive the proportionality relationship between P and T. (b)If a car tire is filled to a pressure of 32.0 lb>in.2 1psi2 measuredat 75 °F, what will be the tire pressure if the tires heat up to120 °F during driving?
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