(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount Δ L when its temperature changes by Δ T , the stress is equal to F A = Y ( Δ L L 0 − α Δ T ) where F is the tension on the rod, L 0 is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends ( Fig. P17.79 ). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but state them. Figure P17.79
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount Δ L when its temperature changes by Δ T , the stress is equal to F A = Y ( Δ L L 0 − α Δ T ) where F is the tension on the rod, L 0 is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends ( Fig. P17.79 ). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but state them. Figure P17.79
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount ΔL when its temperature changes by ΔT, the stress is equal to
F
A
=
Y
(
Δ
L
L
0
−
α
Δ
T
)
where F is the tension on the rod, L0 is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends (Fig. P17.79). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but state them.
A liquid has a density r. (a) Show that the fractional change in density for a change in temperature ΔT is Δρ/ρ = -β ΔT. (b) What does the negative sign signify? (c) Fresh water has a maximum density of 1.000 0 g/cm3 at 4.0°C. At 10.0°C, its density is 0.999 7 g/cm3. What is β for water over this temperature interval? (d) At 0°C, the density of water is 0.999 9 g/cm3. What is the value for β over the temperature range 0°C to 4.00°C?
The vapor pressure is the pressure of the vapor phase of a
substance when it is in equilibrium with the solid or liquid phase of the
substance. The relative humidity is the partial pressure of water vapor in the air
divided by the vapor pressure of water at that same temperature, expressed as a
percentage. The air is saturated when the humidity is 100%. (a) The vapor
pressure of water at 20.0°C is 2.34 × 10³ Pa. If the air temperature is 20.0°C and
the relative humidity is 60%, what is the partial pressure of water vapor in the
atmosphere (that is, the pressure due to water vapor alone)?
The ideal gas law relates the pressure P, volume V, and temperature T of an
ideal gas:
PV = nRT
where n is the number of moles and R = 8.3145 J/(K mol). Plots of pressure
versus volume at constant temperature are called isotherms. Plot the isotherms
for one mole of an ideal gas for volume ranging from 1 to 10 m', at tempera-
tures of T = 100, 200, 300, and 400 K (four curves in one plot). Label the
axes and display a legend. The units for pressure are Pa. n=1
Chapter 17 Solutions
University Physics with Modern Physics (14th Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
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