This chapter explores the thermal properties of matter, focusing on heat, temperature, and heat transfer mechanisms. Understanding these concepts is vital for grasping how energy interacts with materials in various states.
Thermal Properties of Matter – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the Thermal Properties of Matter chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Δl = αl * l₀ * ΔT
Δl is the change in length, αl is the coefficient of linear expansion, l₀ is the original length, and ΔT is the change in temperature. This formula quantifies linear expansion, useful in construction and manufacturing.
ΔA = 2αA₀ * ΔT
ΔA is the change in area, A₀ is the original area, and α is the coefficient of area expansion. It helps understand area expansion in materials like metals and polymers.
ΔV = βV₀ * ΔT
ΔV is the change in volume, β is the coefficient of volume expansion, and V₀ is the original volume. It is useful in fluid mechanics for studying liquids and gases.
Q = mcΔT
Q is the heat added, m is mass, c is specific heat capacity, and ΔT is the change in temperature. This is crucial in calorimetry to determine heat transfer.
L_f = Q/m
L_f is the latent heat of fusion, Q is the heat absorbed or released during the phase change, and m is the mass of the substance. This formula is important for processes involving melting.
L_v = Q/m
L_v is the latent heat of vaporization. Similar to L_f, it describes the heat involved when a substance changes from liquid to vapor, crucial in thermodynamics.
PV = nRT
This ideal gas equation relates pressure (P), volume (V), number of moles (n), and temperature (T) with R as the universal gas constant. It is foundational in thermodynamics.
H = kA(T₁ - T₂)/d
H is the heat transfer rate, k is thermal conductivity, A is the area, T₁ and T₂ are temperatures of two sides, and d is the distance between them. Critical for understanding conduction.
H = eσA(T^4 - T_s^4)
Describes radiation from a surface, where H is the heat emitted, e is the emissivity, σ is the Stefan-Boltzmann constant, A is the area, T is the surface temperature, and T_s is the surrounding temperature.
-dQ/dt = k(T - T_s)
Newton’s Law of Cooling relates the rate of heat loss from an object (dQ/dt) to the temperature difference between the object and its surroundings. Important in thermodynamics and practical cooling applications.
Equations
T_K = T_C + 273.15
Converts Celsius to Kelvin, where T_K is temperature in Kelvin and T_C is temperature in Celsius. Important for aligning different temperature scales.
t_F = (9/5)t_C + 32
Converts Celsius (t_C) to Fahrenheit (t_F). Useful for temperature measurements in various applications.
ΔV/V = α_V * ΔT
Defines volume expansion related to volume change per unit volume for a temperature change ΔT. It's applicable in fluid mechanics and material science.
Q = mL
For changes of state, where Q is the heat supplied, m is mass, and L is latent heat (either fusion or vaporization). Necessary for calculating energy in phase changes.
Q = msΔT
A rearrangement of the specific heat formula that expresses heat transfer in terms of mass and temperature change, essential for calorimetry.
P₁V₁/T₁ = P₂V₂/T₂
For the relationships of different states of a gas, showcasing the variation of pressure, volume, and temperature together. Essential in thermodynamic processes.
ΔT_{average} = (T_{room} - T_{initial}) / time
Equates the average change in temperature per unit time, useful in measuring cooling rates.
λ_m T = constant
Wien’s Displacement Law that highlights the relationship between temperature and the maximum wavelength of radiation for a black body, critical in thermodynamics.
σ = 5.67 x 10^-8 W/m^2 K^4
The Stefan-Boltzmann constant related to body radiation, used in radiation calculations for heat transfer.
α_V = 3 * α_l
Relationship between the coefficient of volume expansion (α_V) and coefficient of linear expansion (α_l). Useful for materials expanding uniformly in three dimensions.
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