We want to construct a thermometer using mercury. As the mercury in the bulb is heated, it expands and moves up the thin capillary tube connected to the bulb. The symbol used for the coefficient of volume expansion of a substance due to a temperature increase is p. It is used in the following equation: ΔV = βV ( ΔT ) Here, Δ V is the increase in volume, V is the original volume, and Δ T is the temperature increase. The value of β for mercury is 1.8 × 10 −4 [1/degree Celsius] . If the bulb contains 0.2 milliliters [mL] and the tube has a diameter of 0.2 millimeters [mm], how much will the mercury rise in the tube in units of centimeters [cm] if we increase the temperature from 30 degrees Fahrenheit [°F] to 70 degrees Fahrenheit [°F]?
We want to construct a thermometer using mercury. As the mercury in the bulb is heated, it expands and moves up the thin capillary tube connected to the bulb. The symbol used for the coefficient of volume expansion of a substance due to a temperature increase is p. It is used in the following equation: ΔV = βV ( ΔT ) Here, Δ V is the increase in volume, V is the original volume, and Δ T is the temperature increase. The value of β for mercury is 1.8 × 10 −4 [1/degree Celsius] . If the bulb contains 0.2 milliliters [mL] and the tube has a diameter of 0.2 millimeters [mm], how much will the mercury rise in the tube in units of centimeters [cm] if we increase the temperature from 30 degrees Fahrenheit [°F] to 70 degrees Fahrenheit [°F]?
Solution Summary: The author calculates the rise of mercury in the tube when the temperature is increased from 30° to 70°.
We want to construct a thermometer using mercury. As the mercury in the bulb is heated, it expands and moves up the thin capillary tube connected to the bulb. The symbol used for the coefficient of volume expansion of a substance due to a temperature increase is p. It is used in the following equation:
ΔV =βV(ΔT)
Here, ΔV is the increase in volume, V is the original volume, and ΔT is the temperature increase. The value of β for mercury is 1.8 × 10−4 [1/degree Celsius] . If the bulb contains 0.2 milliliters [mL] and the tube has a diameter of 0.2 millimeters [mm], how much will the mercury rise in the tube in units of centimeters [cm] if we increase the temperature from 30 degrees Fahrenheit [°F] to 70 degrees Fahrenheit [°F]?
The heated rod from Problem 3 is subject to a volumetric heating
h(x) = h0
x
L in units of [Wm−3], as shown in the figure below. Under the
heat supply the temperature of the rod changes along x with the
temperature function T (x). The temperature T (x) is governed by the
d
following equations:
−
dx (q(x)) + h(x) = 0 PDE
q(x) =−k dT
dx Fourier’s law of heat conduction (4)
where q(x) is the heat flux through the rod and k is the (constant)
thermal conductivity. Both ends of the bar are in contact with a heat
reservoir at zero temperature.
Determine:
1. Appropriate BCs for this physical problem.
2. The temperature function T (x).
3. The heat flux function q(x).
Side Note: Please see that both ends of bar are in contact with a heat reservoir at zero temperature so the boundary condition at the right cannot be du/dx=0 because its not thermally insulated. Thank you
The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω2x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement d u(x) is governed by the following equations: dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L. Determine: 1. Appropriate BCs for this physical problem. 2. The displacement function u(x). 3. The stress function σ(x). SIDE QUESTION: I saw a tutor solve it before but I didn't understand why the tutor did not divide E under the second term (c1x) before finding u(x). The tutor only divided E under first term. please explain and thank you
calculate the total power required to go 80 mph in a VW Type 2 Samba Bus weighing 2310 lbs. with a Cd of 0.35 and a frontal area of 30ft^2. Consider the coefficient of rolling resistance to be 0.018. What is the increase in power required to go the same speed if the weight is increased by 2205 pounds (the rated carrying capacity of the vehicle). If the rated power for the vehicle is 49 bhp, will the van be able to reach 80 mph at full carrying capacity?
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