Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of the gas is
To find the isothermal bulk modulus K of an ideal gas we can use the formula: K = - V (∂P/∂V)_T For an ideal gas at constant temperature (isothermal) the relation between pressure P and volume V is given by Boyle's Law: PV = nRT Differentiating this equation while keeping the temperature constant giRead more
To find the isothermal bulk modulus K of an ideal gas we can use the formula:
K = – V (∂P/∂V)_T
For an ideal gas at constant temperature (isothermal) the relation between pressure P and volume V is given by Boyle’s Law:
PV = nRT
Differentiating this equation while keeping the temperature constant gives us:
∂P/∂V = -nRT/V²
Thus the isothermal bulk modulus becomes:
K = -V (-nRT/V²) = nRT/V
Since nRT = PV we can substitute that in the equation too;
K = PV/V = P
Thus the isothermal bulk modulus of the gas is:
K = P
Click for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/
A wire of length L, and cross-sectional area A is made of a material of Young’s modulus Y. If the wire is stretched by an amount x, the work done is
To calculate the work done W by stretching a wire of length L and cross-sectional area A through an amount x, we could use the following relationship between stress strain and Young's modulus: The stress in the wire, σ, can be found by the relation as follows: σ = F/A where F represents the appliedRead more
To calculate the work done W by stretching a wire of length L and cross-sectional area A through an amount x, we could use the following relationship between stress strain and Young’s modulus:
The stress in the wire, σ, can be found by the relation as follows:
σ = F/A
where F represents the applied force. The strain ε is described by:
ε = x/L
As related by Young’s modulus Y,
Y = σ/ε = (F/A)/(x/L)
From this we can write the force F:
F = (YAx)/L
The work done W when the wire is stretched by an amount x is given by the area under the stress-strain curve which is the integral of force over displacement:
W = ∫ F dx = ∫ (YAx/L) dx
Evaluating the integral we get:
W = (Y A/L) ∫ x dx = (Y A/L) * [x²/2] from 0 to x = (Y A/L) * (x²/2)
Work done is hence,
W = (Y A x²)/(2 L)
Click for more solutions:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/
Define the term strain. Why it has no units and dimensions? What are different types of strain?
Definition of Strain: Strain is a measure of deformation, which gives the displacement between the particles in a material body. Strain is defined as the ratio of change in dimension to the original dimension of the material. In mathematical terms, strain (ε) is expressed as: ε = ΔL / L₀ Here, ΔLRead more
Definition of Strain:
Strain is a measure of deformation, which gives the displacement between the particles in a material body. Strain is defined as the ratio of change in dimension to the original dimension of the material. In mathematical terms, strain (ε) is expressed as:
ε = ΔL / L₀
Here, ΔL represents the change in length and L₀ represents the original length.
Why Strain Has No Units and Dimensions:
Strain is a dimensionless quantity because it is a ratio of two lengths (change in length to original length), which means that both numerator and denominator have the same units. Hence, the units cancel out, and one gets a unitless value. Since it is dimensionless, therefore it has no dimensions in the context of physical measurement.
Different Types of Strain:
1. Tensile Strain: It takes place when a material is stretched. It is defined as the change in length divided by the original length (elongation).
2. Compressive Strain: It takes place when a material is compressed. It is defined as the change in length divided by the original length (shortening).
3. Shear Strain: It is that strain which arises due to shear forces applied on a material. It is defined as the change in angle between two lines originally at right angles, expressed as the ratio of lateral displacement to the original length.
4. Volumetric Strain: It is the change in volume per unit original volume of a material, occurring under uniform pressure.
These types of strain are important for understanding how materials respond to various forces and deformations.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/
Define the term stress. Give its units and dimensions. Describe the different types of stress.
Definition of Stress: Stress is defined as the force exerted per unit area within materials. It results from external forces applied to an object, resulting in deformation. Mathematically, stress is represented as σ = F / A where σ is the stress F is the applied force and A is the cross-sectional arRead more
Definition of Stress:
Stress is defined as the force exerted per unit area within materials. It results from external forces applied to an object, resulting in deformation. Mathematically, stress is represented as
σ = F / A
where σ is the stress F is the applied force and A is the cross-sectional area over which the force is applied.
Units:
The SI unit of stress is Pascal (Pa), which is equivalent to Newton per square meter (N/m²).
Dimensions:
The dimensions of stress are represented as [M L⁻² T⁻²], where M is mass, L is length, and T is time.
Different Types of Stress:
1. Tensile Stress: This takes place when any material undergoes stretching or pull forces. The force per unit area along the direction of an applied force defines it.
2. Compressive Stress: It arises when compressive forces compress or squeeze the material. Force per unit area in a direction opposite to an applied force is defined by compressive stress.
3. Shear Stress: It happens when a material is subjected to forces that cause one layer of the material to slide over another. It is the force applied parallel to the surface divided by the area of the surface.
4. Volumetric Stress: This stress is due to changes in volume because of uniform pressure applied in all directions. It is significant in fluid mechanics and materials science.
Understanding these different types of stress is important in analyzing material behavior under various loading conditions.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/
Explain elastic behaviour of solids on the basis of mechanical spring-ball model of a solid.
Elasticity of Solids: Elastic behavior refers to the phenomenon of an ability to regain the original configuration shape and size when the applied external force is removed. This is critical in understanding how a material deforms and recovers under stress. The mechanical spring-ball model is a usefRead more
Elasticity of Solids:
Elastic behavior refers to the phenomenon of an ability to regain the original configuration shape and size when the applied external force is removed. This is critical in understanding how a material deforms and recovers under stress. The mechanical spring-ball model is a useful representation to explain this concept.
Mechanical Spring-Ball Model:
1. Basic Concept: In a mechanical spring-ball model, atoms or molecules in a solid can be visualized as balls held together by springs. The springs are equivalent to the interatomic forces or bonding forces between the atoms.
2. Elastic Deformation: When external force is applied to the solid, balls go a little away from their equilibrium positions; as a result springs stretch or compress because of which elastic deformation takes place. In this type of deformation, the shape of the material changes, but the material remains intact.
3. Restoring Forces: When the applied force is withdrawn, the springs exert restoring forces that restore the balls to their original positions. This is because the interatomic forces are elastic in nature; the material can return to its original shape and size.
4. Elastic Limit: Elastic behavior is seen up to a certain limit called the elastic limit. If the applied force exceeds this limit, then the springs might get permanently deformed and the deformation will be plastic. In this case, the solid cannot regain its original shape.
5. Mathematical Representation: This elastic region has a relationship that can be stated using Hooke’s Law that relates stress as proportional to strain (σ = Eε, where E is the modulus of elasticity).
In this mechanical model of a spring-ball, interatomic forces and arrangements of atoms come into play about deformation and recovery characteristics of the solids under stress.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/