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Define heat current and thermal resistance. Write mathematical expressions for them in terms of thermal conductivity K.
Heat Current (Q): Heat current refers to the rate at which heat energy flows through a material. It depends on the temperature difference across the material, its area, the length of the material, and its thermal conductivity. Mathematical Expression for Heat Current: The heat current Q is given byRead more
Heat Current (Q):
Heat current refers to the rate at which heat energy flows through a material. It depends on the temperature difference across the material, its area, the length of the material, and its thermal conductivity.
Mathematical Expression for Heat Current:
The heat current Q is given by Fourier’s Law of Heat Conduction:
Q = (K A (T1 – T2)) / L
Where:
– Q = Heat current (rate of heat flow) in watts (W)
– K = Thermal conductivity of the material (W/m·K)
– A = Cross-sectional area through which heat flows (m²)
– T1 – T2 = Temperature difference between the two ends of the material (K or °C)
– L = Length of the material through which heat flows (m)
Thermal Resistance (R):
Thermal resistance is a measure of a material’s resistance to the flow of heat. It depends on the material’s thermal conductivity, length, and area.
Mathematical Expression for Thermal Resistance:
The thermal resistance R is given by:
R = L / (K A)
Where:
– R = Thermal resistance (K·m²/W)
– L = Length of the material (m)
– K = Thermal conductivity of the material (W/m·K)
– A = Cross-sectional area (m²)
Relationship Between Heat Current and Thermal Resistance:
Using the expression for thermal resistance, the heat current can also be written as:
Q = (T1 – T2) / R
Where R is the thermal resistance of the material. This shows that heat current is directly proportional to the temperature difference and inversely proportional to the thermal resistance.
Summary:
– Heat current is the rate of heat transfer through a material, given by Q = (K A (T1 – T2)) / L.
– Thermal resistance is the resistance to heat flow, given by R = L / (K A).
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What do you mean by variable state and steady state in thermal conduction? Define temperature gradient.
Variable State in Thermal Conduction In thermal conduction, a variable state refers to a situation where the temperature distribution within the material is changing with time. In this state, the temperature at any point in the material is not constant, and the heat flow is not steady. This usuallyRead more
Variable State in Thermal Conduction
In thermal conduction, a variable state refers to a situation where the temperature distribution within the material is changing with time. In this state, the temperature at any point in the material is not constant, and the heat flow is not steady. This usually occurs when the material is initially heated or cooled, and the temperature difference between different parts of the material is evolving over time until it reaches equilibrium.
– For instance, suppose a metal rod is heated on one end; the temperature changes at different points along the rod with time since heat is being transferred from the hot end to the cooler end. The gradient will be high in the beginning, and with the passage of time, the gradient will decrease to the point when the system achieves equilibrium.
Steady State in Thermal Conduction:
In thermal conduction, a steady state is when the temperature distribution in the material becomes constant over time. The temperature at any point in the material no longer changes, which means there is no further change in temperature with respect to time. The heat flow becomes constant, and the system has reached thermal equilibrium.
Example: For instance, if the temperature has stabilized such that no temperature variation is noticed in the rod as described earlier, then the system is in a steady state. The amount of heat going into one end is the same as the amount of heat going out the other end.
Temperature Gradient:
Temperature gradient is the measure of how temperature changes over a given distance in a material. It is defined as the rate of change of temperature with respect to distance. It is often measured in units of °C/m or K/m.
– Mathematical Expression: The temperature gradient ∇T can be mathematically expressed as:
∇T = ΔT / Δx
Where:
– ∇T = Temperature gradient (°C/m or K/m)
– ΔT = Temperature difference between two points in the material (°C or K)
– Δx = Distance between the two points (m)
In a steady-state conduction, the temperature gradient is constant and linear, so that the rate of temperature change is uniform throughout the material. In a variable state, the temperature gradient changes with time as the material approaches a new thermal equilibrium.
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What is a thermo-nuclear reaction?
A thermonuclear reaction is a nuclear fusion process in which light nuclei combine to form heavier nuclei at extremely high temperatures, releasing vast amounts of energy. It powers stars, including the Sun, and hydrogen bombs. For more visit here: https://www.tiwariacademy.com/ncert-solutions/classRead more
A thermonuclear reaction is a nuclear fusion process in which light nuclei combine to form heavier nuclei at extremely high temperatures, releasing vast amounts of energy. It powers stars, including the Sun, and hydrogen bombs.
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What is the effect of pressure on the boiling point of a liquid. Explain it with the help of a simple experiment.
Effect of Pressure on the Boiling Point of a Liquid: The boiling point of a liquid is that temperature at which its vapor pressure becomes equal to the external pressure acting on it. When the pressure is increased, the boiling point of the liquid also increases, and when the pressure is decreased,Read more
Effect of Pressure on the Boiling Point of a Liquid:
The boiling point of a liquid is that temperature at which its vapor pressure becomes equal to the external pressure acting on it. When the pressure is increased, the boiling point of the liquid also increases, and when the pressure is decreased, the boiling point decreases. This is because a high pressure requires much energy (heat) to enable the liquid molecules to escape into the vapor phase, while a low pressure will make it easier to vaporize.
Explanation Using a Simple Experiment
To understand how pressure affects the boiling point of a liquid, you can perform a simple experiment using a saucepan, a thermometer, and a vacuum pump or a simple setup to create a change in pressure.
Experiment:
1. Materials Needed:
– A saucepan or beaker
– A thermometer
– A vacuum pump (for lowering pressure) or a pressure cooker (for increasing pressure)
– Water or another liquid (such as alcohol)
2. Procedures:
Experiment 1 (Effect of Decreasing Pressure):
1. Put water in the saucepan and place it on a heat source.
2. Dip the thermometer into the water and measure the temperature.
3. Boil the water and note the temperature at which it starts boiling. The boiling point of water at atmospheric pressure is usually about 100°C.
4. Reduce the pressure using a vacuum pump. Alternatively, you can do this in a simple vacuum chamber, if available.
5. Notice that the water starts boiling at a temperature less than 100°C as the pressure is reduced.
Experiment 2: Effect of Increasing Pressure
1. Repeat the same setup but use a pressure cooker instead of the open saucepan.
2. When the pressure cooker is sealed, it increases the pressure inside.
3. You will notice that as the pressure is increased, it takes longer for the water to boil, and the boiling point is above 100°C.
3. Observations:
– In Experiment 1, as the pressure inside the chamber decreases, the water boils at a temperature lower than its normal boiling point (100°C at 1 atmosphere).
In Experiment 2, the higher temperature at which the water boils results from the increased pressure inside the pressure cooker.
Explanation in Science Terms:
At Low Pressure: Fewer air molecules exert force on the liquid’s surface when pressure is low, so it’s easier for liquid molecules to go into the vapor phase. In this case, the liquid will boil at a lower temperature. That is why water boils at a lower temperature at high altitude where the pressure of the atmosphere is low.
– At Higher Pressure: When the pressure is increased (like in a pressure cooker), the liquid’s vapor pressure needs to overcome a higher external pressure to escape into the gas phase. Therefore, the liquid boils at a higher temperature to provide the necessary energy for the molecules to break free from the liquid phase.
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What do you mean by change of state of a substance?
A change of state is the transformation of a substance from one physical phase or state of matter to another. The three most common states of matter are solid, liquid, and gas. A substance can change between these states due to the addition or removal of heat energy. The change of state involves chaRead more
A change of state is the transformation of a substance from one physical phase or state of matter to another. The three most common states of matter are solid, liquid, and gas. A substance can change between these states due to the addition or removal of heat energy. The change of state involves changes in the arrangement and energy of the particles (atoms or molecules) that make up the substance.
Types of Changes of State:
1. Melting (Solid to Liquid):
– When the solid is heated, the energy of the particles increases, causing them to move more freely until they break away from each other. The end result is the solid turns to liquid.
Example: Ice turns to water due to melting.
2. Freezing (Liquid to Solid):
– When a liquid is cooled, the particles lose energy and move slowly; thus, they can form bonds and arrange themselves in an orderly structure to make the liquid become a solid.
Example: Water freezes to ice.
3. Vaporization (Liquid to Gas):
This happens when a liquid is heated; the particles receive enough energy so that they would be able to overcome the forces holding them in place, break free, and escape into the gas phase by vaporization. Included in this are evaporation through the surface of a liquid at any temperature, and boiling that occurs throughout a liquid at specific temperatures. Example: boiling water into steam.
4. Condensation from Gas to Liquid
– When a gas is cooled, the particles lose energy, slow down, and come closer together, forming liquid droplets.
Example: Water vapor condensing on a cold surface.
5. Sublimation (Solid to Gas):
– Change of phase from solid directly to gas, bypassing the liquid phase. This takes place when the solid particles acquire sufficient energy to break free from their bonds, dispersing themselves as gas particles.
– Dry ice is the solid carbon dioxide sublimating to carbon dioxide gas.
6. Deposition (Gas to Solid):
– Deposition is the opposite of sublimation, where a gas transforms directly into a solid without going through the liquid phase. This happens when gas particles lose enough energy to settle into a solid structure.
Example: Frost forming from water vapor in the air.
Factors Affecting the Change of State:
– Temperature: The addition of heat energy raises the temperature, and the substance can change from solid to liquid or from liquid to gas, such as melting or vaporization. Cooling the substance will cause the opposite changes, like freezing or condensation.
Pressure applied to a substance can also be a variable. For example, increasing the pressure can make a gas condense into a liquid or even a liquid freeze into a solid.
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