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Using the following system, find the temperature at the copper/steel and steel/…

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Wize University Physics Textbook (Master) > Heat and Temperature

Heat Transfer: Conductors in Series and Parallel

3 Activities

Using the following system, find the temperature at the copper/steel and steel/aluminum interfaces. What is the heat flow through each material? You may assume only conduction occurs, and that the fixed ends are held at constant temperature.


Givens:
ksteel=43[WmK], kCu=401[WmK], kal=205[WmK]k_{steel}=43\left[\frac{W}{mK}\right],\ k_{Cu}=401\left[\frac{W}{mK}\right],\ k_{al}=205\left[\frac{W}{mK}\right]

Lsteel=1[m], LCu=2.4[m], Lal=2.0[m]L_{steel}=1\left[m\right],\ L_{Cu}=2.4\left[m\right],\ L_{al}=2.0\left[m\right]

TH=300°C, TC=100°CT_H=300\degree C,\ T_C=100\degree C
More Heat Transfer: Conductors in Series and Parallel Questions:
Consider a double-pane window (4mm glass layers, 20mm gap between them). When it is 20 degrees Celsius inside and -15 degrees Celsius outside, and if the area of the windows is 1 m2,
a) What is the energy loss if the gap is filled with air?
b) What if the gap is filled with Argon instead?
Single-pane windows consist of a single layer of glass. They are light, but double-pane windows are much more energy-efficient; they have a layer of air between two thin layers of glass. In very cold places such as Yellowknife, you may also come across triple-pane windows.
Consider these windows when it is 20 degrees Celsius inside and -40 degrees Celsius outside. The area of the windows is 1 m2.
a) What is the energy loss if a single-pane window was used? (2.2 mm thick glass)
Why are double pane windows more effective at preventing heat loss than single pane windows of the same thickness? Draw a diagram to demonstrate this property.
How much more effective are double pane windows are if kglass=1.05[WmK]k_{glass}=1.05\left[\frac{W}{mK}\right], kair=0.025[WmK]k_{air}=0.025\left[\frac{W}{mK}\right]. The single pane is 7 mm7\ mmthick, and the double panes are 3 mm3\ mmthick (air accounts for the remaining 1 mm1\ mm).
If we could vacuum pump the double pane window, what could happen to the heat flow through the window?
A home has 4 walls, three of the walls have no window and are made of a layer 1m thick wood and a layer of 1m thick brick. Each wall is 2 meter by 2 meters and the window on one of the walls is 1 meter by 1 meter. The window is a double panned window which means its a 0.5 m layer of glass then 1 m layer of air then a 0.5 m layer of glass. Each wall is also 2 meters thick. If the inside temperature is 20°C20\degree C and the outside temperature is 0°C0\degree C. (Do not consider the roof or floor).
What is the power level that a generator need to provide such that the inside temperature stays at 20°C20\degree C, if the generator is only 70% efficient.
K wood: 0.12 wm⋅k\frac{w}{m\cdot k}
New Practice Question
A compound bar made up of 15cm of Cu with ACu=25cm2A_{Cu}=25cm^{2} and 20 cm of steel with ASt=10cm2A_{St}=10cm^2𝑎𝑡 𝑇 = 293𝐾 is fixed at both ends as shown in the diagram below. How much is the stress in each metal if the system is heated uniformly by a 700 watt heater for 5 minutes?
CCu=390JKg⋅KCSt=470JKg⋅KYCu=11×1010Nm2YSt=20×1010Nm2aCu=1.7×10−51KaSt=1.2×10−51KρCu=9gcm3ρSt=7.85gcm3\begin{array}{cc}C_{Cu}=390 \frac{J}{Kg\cdot K}&C_{St}=470\frac{J}{Kg\cdot K}\\Y_{Cu}=11\times 10^{10} \frac{N}{m^2}&Y_{St}=20\times 10^{10} \frac{N}{m^2}\\a_{Cu}=1.7\times 10^{-5}\frac{1}{K}&a_{St}=1.2\times 10^{-5}\frac{1}{K}\\\rho_{Cu}=9\frac{g}{cm^3}&\rho_{St}=7.85\frac{g}{cm^3}\end{array}