The coefficient of cubical expansion (β) of a substance is the fractional change in its volume for a unit change in temperature, when the substance is heated or cooled at constant pressure. Mathematically, it is defined as: β = (1/V) * (dV/dT) where: - β is the coefficient of cubical expansion, - VRead more
The coefficient of cubical expansion (β) of a substance is the fractional change in its volume for a unit change in temperature, when the substance is heated or cooled at constant pressure.
Mathematically, it is defined as:
β = (1/V) * (dV/dT)
where:
– β is the coefficient of cubical expansion,
– V is the initial volume,
– dV is the change in volume,
– dT is the change in temperature.
The units of β are per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹).
We know that for an ideal gas at constant pressure, the volume is given by V = nRT where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature. Now, for a small change in temperature, the change in volume can be written as: dV = βV dT where βRead more
We know that for an ideal gas at constant pressure, the volume is given by
V = nRT
where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature.
Now, for a small change in temperature, the change in volume can be written as:
dV = βV dT
where β is the coefficient of cubical expansion and dT is the change in temperature.
From the equation of state, V = nRT, we have:
dV = nR dT
Comparing the two expressions for dV, we get:
βV = nR / V
Since V = nRT, we can substitute this into the above equation:
β = 1 / T
Therefore, the coefficient of cubical expansion β for an ideal gas at constant pressure is equal to the reciprocal of its absolute temperature.
The platinum resistance thermometer works on the principle that the electrical resistance of platinum is a changing function of temperature. The thermometer is a platinum wire whose resistance varies linearly with temperature. The resistance is measured using a Wheatstone bridge or other precise cirRead more
The platinum resistance thermometer works on the principle that the electrical resistance of platinum is a changing function of temperature.
The thermometer is a platinum wire whose resistance varies linearly with temperature. The resistance is measured using a Wheatstone bridge or other precise circuit. By calibrating the resistance at known temperatures, the thermometer can determine an unknown temperature. Platinum is used because of its stability, wide temperature range, and predictable resistance-temperature relationship.
A liquid thermometer is a type of thermometer that measures temperature through the expansion and contraction of a liquid in response to temperature changes. In general, the liquid is held within a sealed glass tube with a calibrated scale. Advantages of using mercury 1. It has a very high boiling pRead more
A liquid thermometer is a type of thermometer that measures temperature through the expansion and contraction of a liquid in response to temperature changes. In general, the liquid is held within a sealed glass tube with a calibrated scale.
Advantages of using mercury
1. It has a very high boiling point and a low freezing point; thus, it can measure a wide range of temperatures.
2. It does not wet the glass, hence ensuring accurate readings.
3. Mercury expands uniformly with temperature changes, so it is very accurate.
4. It is visible because of its shiny, metallic appearance.
Joule's Law of Equivalence between Work and Heat: It states that the amount of heat produced in a conductor due to an electric current is directly proportional to the square of the current (I), the resistance (R) of the conductor, and the time (t) for which the current flows. It can be represented mRead more
Joule’s Law of Equivalence between Work and Heat: It states that the amount of heat produced in a conductor due to an electric current is directly proportional to the square of the current (I), the resistance (R) of the conductor, and the time (t) for which the current flows. It can be represented mathematically as:
Q = I²Rt
This law also implies that work and heat are interchangeable, in other words, work done on a system can be converted into heat, and vice-versa.
### Mechanical Equivalent of Heat:
The **mechanical equivalent of heat** is the amount of mechanical work that has to be expended to produce a unit of heat. It is a measure of the relationship between mechanical energy (work) and thermal energy (heat). The most common unit used to express this is **Joules per calorie**.
It is defined as the amount of work (in Joules) required to produce 1 calorie of heat. The mechanical equivalent of heat is approximately:
1 calorie = 4.18 Joules
It means that to produce 1 calorie of heat, 4.18 Joules of mechanical work is required. This establishes the equivalence between mechanical energy and heat energy.
Define coefficient of cubical expansion. Write an expression for it. Give its units.
The coefficient of cubical expansion (β) of a substance is the fractional change in its volume for a unit change in temperature, when the substance is heated or cooled at constant pressure. Mathematically, it is defined as: β = (1/V) * (dV/dT) where: - β is the coefficient of cubical expansion, - VRead more
The coefficient of cubical expansion (β) of a substance is the fractional change in its volume for a unit change in temperature, when the substance is heated or cooled at constant pressure.
Mathematically, it is defined as:
β = (1/V) * (dV/dT)
where:
– β is the coefficient of cubical expansion,
– V is the initial volume,
– dV is the change in volume,
– dT is the change in temperature.
The units of β are per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹).
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Show that the coefficient of cubical expansion of an ideal gas at constant pressure is equal to the reciprocal of its absolute temperature.
We know that for an ideal gas at constant pressure, the volume is given by V = nRT where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature. Now, for a small change in temperature, the change in volume can be written as: dV = βV dT where βRead more
We know that for an ideal gas at constant pressure, the volume is given by
V = nRT
where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature.
Now, for a small change in temperature, the change in volume can be written as:
dV = βV dT
where β is the coefficient of cubical expansion and dT is the change in temperature.
From the equation of state, V = nRT, we have:
dV = nR dT
Comparing the two expressions for dV, we get:
βV = nR / V
Since V = nRT, we can substitute this into the above equation:
β = 1 / T
Therefore, the coefficient of cubical expansion β for an ideal gas at constant pressure is equal to the reciprocal of its absolute temperature.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
Describe the working principle of a platinum resistance thermometer.
The platinum resistance thermometer works on the principle that the electrical resistance of platinum is a changing function of temperature. The thermometer is a platinum wire whose resistance varies linearly with temperature. The resistance is measured using a Wheatstone bridge or other precise cirRead more
The platinum resistance thermometer works on the principle that the electrical resistance of platinum is a changing function of temperature.
The thermometer is a platinum wire whose resistance varies linearly with temperature. The resistance is measured using a Wheatstone bridge or other precise circuit. By calibrating the resistance at known temperatures, the thermometer can determine an unknown temperature. Platinum is used because of its stability, wide temperature range, and predictable resistance-temperature relationship.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
What is a liquid thermometer ? What are the advantages of using mercury as a thermometric substance over liquids?
A liquid thermometer is a type of thermometer that measures temperature through the expansion and contraction of a liquid in response to temperature changes. In general, the liquid is held within a sealed glass tube with a calibrated scale. Advantages of using mercury 1. It has a very high boiling pRead more
A liquid thermometer is a type of thermometer that measures temperature through the expansion and contraction of a liquid in response to temperature changes. In general, the liquid is held within a sealed glass tube with a calibrated scale.
Advantages of using mercury
1. It has a very high boiling point and a low freezing point; thus, it can measure a wide range of temperatures.
2. It does not wet the glass, hence ensuring accurate readings.
3. Mercury expands uniformly with temperature changes, so it is very accurate.
4. It is visible because of its shiny, metallic appearance.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
State Joule’s law of equivalence between work and heat. Hence define mechanical equivalent of heat.
Joule's Law of Equivalence between Work and Heat: It states that the amount of heat produced in a conductor due to an electric current is directly proportional to the square of the current (I), the resistance (R) of the conductor, and the time (t) for which the current flows. It can be represented mRead more
Joule’s Law of Equivalence between Work and Heat: It states that the amount of heat produced in a conductor due to an electric current is directly proportional to the square of the current (I), the resistance (R) of the conductor, and the time (t) for which the current flows. It can be represented mathematically as:
Q = I²Rt
This law also implies that work and heat are interchangeable, in other words, work done on a system can be converted into heat, and vice-versa.
### Mechanical Equivalent of Heat:
The **mechanical equivalent of heat** is the amount of mechanical work that has to be expended to produce a unit of heat. It is a measure of the relationship between mechanical energy (work) and thermal energy (heat). The most common unit used to express this is **Joules per calorie**.
It is defined as the amount of work (in Joules) required to produce 1 calorie of heat. The mechanical equivalent of heat is approximately:
1 calorie = 4.18 Joules
It means that to produce 1 calorie of heat, 4.18 Joules of mechanical work is required. This establishes the equivalence between mechanical energy and heat energy.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/