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Two identical rods are connected between two containers. One of them is at 100°C and another is at 0° C. If rods are connected in parallel then the rate of melting of ice is q₁g/sec. If they are connected in series then the rate is q₂. The ratio q₂/q₁ is
When two rods are connected in parallel, both rods contribute equally to the heat transfer, which results in a higher overall rate of heat transfer (hence, higher melting rate of ice). When two rods are connected in series, the heat has to pass through both rods sequentially. This effectively reduceRead more
When two rods are connected in parallel, both rods contribute equally to the heat transfer, which results in a higher overall rate of heat transfer (hence, higher melting rate of ice).
When two rods are connected in series, the heat has to pass through both rods sequentially. This effectively reduces the rate of heat transfer compared to the parallel arrangement. The heat flow through the system will be limited by the rod with the lower heat transfer rate, reducing the overall rate of melting.
The rate of heat transfer is inversely proportional to the total resistance (or thermal resistance) in the system. The effective resistance is lower than that in the series case; thus, there will be a greater rate of heat transfer in the parallel case.
The ratio of the rates of melting q₂/q₁, when connected in series to parallel, is thus 1/2.
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An ideal black body at room temperature is thrown into furnace. It is observed that
An ideal black body at room temperature absorbs all the incident radiations and therefore appears black. It begins emitting thermal radiation after heating in a furnace and then increases in brightness with increasing temperatures. An ideal black body would emit radiation dependent on its temperaturRead more
An ideal black body at room temperature absorbs all the incident radiations and therefore appears black. It begins emitting thermal radiation after heating in a furnace and then increases in brightness with increasing temperatures. An ideal black body would emit radiation dependent on its temperature and thus, be brightest when heated to its higher temperatures.
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A wall has two layers A and B, each made of a different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36°C. The temperature difference across the layer A
This is a two-layer wall, where A and B represent different materials. The same thickness is taken for both the layers, while the thermal conductivity of material A is twice that of material B. Under the conditions of thermal equilibrium, the total temperature difference between the two layers is 36Read more
This is a two-layer wall, where A and B represent different materials. The same thickness is taken for both the layers, while the thermal conductivity of material A is twice that of material B. Under the conditions of thermal equilibrium, the total temperature difference between the two layers is 36°C. As the rate of heat transfer between both the layers should be equal, the temperature difference between both the layers depends on their respective thermal conductivities.
Because material A’s thermal conductivity is higher, there will be relatively easier passage of heat through material A than through B. Therefore the temperature difference shall be smaller when measured across the layer A and larger when calculated across layer B. Since material A has two times the thermal conductivity of B the temperature difference while measured across material A will therefore be half measured across material B.
We have the total temperature difference across the wall, which is 36°C, and we know that the temperature difference across layer B is greater. So we can say that the temperature difference across layer A is 12°C.
So, the temperature difference across layer A is 12°C.
See lessIn which of the following processes, convection does not take place primarily?
In this case, the primary mode of heat transfer is radiation, since the filament emits thermal radiation that heats the surrounding air and the glass of the bulb. Convection primarily occurs when the heated fluid (like air or water) moves due to temperature differences, but this is not the primary pRead more
In this case, the primary mode of heat transfer is radiation, since the filament emits thermal radiation that heats the surrounding air and the glass of the bulb. Convection primarily occurs when the heated fluid (like air or water) moves due to temperature differences, but this is not the primary process in the case of a light bulb.
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Explain the distribution of energy in the spectrum of a black body. What conclusions can be drawn from it?
The energy distribution in the spectrum of a black body is defined as the dependency of the intensity of the radiated energy emitted by a perfect absorber and emitter of radiation, a black body, on wavelength and temperature. This distribution is described by Planck's law and obeys the following conRead more
The energy distribution in the spectrum of a black body is defined as the dependency of the intensity of the radiated energy emitted by a perfect absorber and emitter of radiation, a black body, on wavelength and temperature. This distribution is described by Planck’s law and obeys the following conditions:
1. Wavelength Dependence: The radiation intensity of a black body at any given temperature depends on the wavelength. Initially, it increases with decreasing wavelength up to a point, then levels off and drops as the wavelength increases further. The peak in intensity shifts towards shorter wavelengths with increasing temperature.
2. Peak Wavelength Shift: According to Wien’s displacement law, the wavelength at which the radiation intensity is maximum is inversely proportional to the temperature of the black body. This means as the temperature of the body increases, the peak of its emission spectrum shifts towards shorter wavelengths (higher frequencies).
3. Total Energy Emission: According to Stefan-Boltzmann law, the total energy emitted per unit surface area of the black body is proportional to the fourth power of its absolute temperature. So, with an increase in temperature, the total energy emitted by the black body increases considerably.
4. Infrared to Ultraviolet: Most radiation from a black body is infrared at the lower temperatures that are not visible. As temperature rises, radiation comes into the range of visible colors, and beyond that temperature the radiation shifts towards ultraviolet, and even above that to various other parts in the electromagnetic spectrum.
Inferences Based on the Black Body Spectrum:
1. Black Body Radiation Depends Only on Temperature Black body radiation’s intensity and spectrum depend entirely on the temperature, according to Planck’s law. The more energetic a black body is, the higher the energy that will be emitted from it and the shorter the wavelength of the maximum emission.
2. Energy is Quantized: The distribution of energy shows the quantized nature of energy levels, as evidenced by Planck’s law, which was one of the key developments that led to the foundation of quantum theory.
3. Ideal Absorber and Emitter: A black body absorbs all falling radiation and then re- emits it in a particular spectrum. This is helpful to understand energy exchanges in systems like stars, earth’s atmosphere, and thermal radiation.
4. Wien’s and Stefan-Boltzmann Laws: This explains the relationship between temperature and radiation, clarifying phenomena ranging from the color of stars-which actually represents their temperature-to the thermal radiation an object throws off.
Black body radiation’s spectrum ensures to explain and quantify the interaction of matter with electromagnetic radiation, leading to important insights into thermodynamics and quantum mechanics.
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