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Chapter 19: Problem 7

A bimetallic strip is constructed from strips of two different metals that are bonded along their lengths. Explain how such a device may be used in a thermostat to regulate temperature.

Short Answer

Expert verified
Answer: A bimetallic strip, made of two metals with different coefficients of thermal expansion, bends upon temperature changes. In a thermostat, this bending motion activates or deactivates a switch, controlling the heating or cooling system and maintaining the desired temperature.

Step by step solution

01

Understand the structure of a bimetallic strip

A bimetallic strip is made of two metals with different coefficients of thermal expansion, meaning that they expand at different rates when heated. These metals are bonded together along their length, forming a single strip. When heated, the metal with the higher coefficient of thermal expansion will expand more, causing the bimetallic strip to bend or curve. The same process occurs in the opposite direction when the strip is cooled.
02

Understand the operation of a thermostat

A thermostat is a device used to maintain a desired temperature in a system, such as heating or cooling systems. It does this by switching the system on and off based on the temperature. When the temperature goes too high or too low, the thermostat triggers an action, such as activating the heating or cooling process, to bring the temperature back to the desired level.
03

Application of the bimetallic strip in a thermostat

In a thermostat, the bimetallic strip is used as the temperature-sensitive element. This means that the thermostat uses the bending or curving motion induced by the temperature change in the bimetallic strip to control the on and off switching of the heating or cooling system.
04

Explain the functioning of a thermostat with the bimetallic strip

When the temperature increases, the bimetallic strip bends towards the side of the metal with a lower coefficient of thermal expansion. This bending action activates a switch in the thermostat, which then turns off the heating process. Conversely, when the temperature decreases, the bimetallic strip bends the other way, deactivating the switch and turning on the heating process. This cycle continues, maintaining the desired temperature within the system. In summary, a bimetallic strip, due to its temperature-dependent bending properties, acts as a temperature-sensitive element in a thermostat, allowing for the regulation of temperature in heating and cooling systems.

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Most popular questions from this chapter

Briefly explain why the thermal conductivities are higher for crystalline than noncrystalline ceramics.

The difference between the specific heats at constant pressure and volume is described by the expression $$c_{p}-c_{v}=\frac{\alpha_{v}^{2} v_{0} T}{\beta}\quad\quad\quad\quad\quad(19.10)$$ where \(\alpha_{v}\) is the volume coefficient of thermal expansion, \(v_{0}\) is the specific volume (i.e., volume per unit mass, or the reciprocal of density \(), \beta\) is the compressibility, and \(T\) is the absolute temperature. Compute the values of \(c_{v}\) at room temperature \((293 \mathrm{K})\) for aluminum and iron using the data in Table 19.1, assuming that \(\alpha_{v}=3 \alpha_{l}\) and given that the values of \(\beta\) for \(A l\) and \(F e\) are \(1.77 \times 10^{-11}\) and \(2.65 \times 10^{-12}(\mathrm{Pa})^{-1},\) respectively.

Nonsteady-state heat flow may be described by the following partial differential equation: $$\frac{\partial T}{\partial t}=D_{T} \frac{\partial^{2} T}{\partial x^{2}}$$ where \(D_{T}\) is the thermal diffusivity; this expression is the thermal equivalent of Fick's second law of diffusion (Equation 5.4b). The thermal diffusivity is defined according to $$D_{T}=\frac{k}{\rho c_{p}}$$ In this expression, \(k, \rho,\) and \(c_{p}\) represent the thermal conductivity, the mass density and the specific heat at constant pressure, respectively. (a) What are the SI units for \(D_{T} ?\) (b) Determine values of \(D_{T}\) for copper brass, magnesia,fused silica, polystyrene, and polypropylene using the data in Table 19.1. Density values are included in Table B.1, Appendix B.

To what temperature must a cylindrical rod of tungsten \(15.025 \mathrm{mm}\) in diameter and a plate of 1025 steel having a circular hole \(15.000 \mathrm{mm}\) in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is \(25^{\circ} \mathrm{C}\).

A \(0.4 \mathrm{m}(15.7 \text { in. })\) rod of a metal elongates \(0.48 \mathrm{mm}(0.019 \text { in. })\) on heating from 20 to \(100^{\circ} \mathrm{C}\left(68 \text { to } 212^{\circ} \mathrm{F}\right) .\) Determine the value of the linear coefficient of thermal expansion for this material.
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