The Ever-Evolving World of Science – Formula & Equation Sheet
Essential formulas and equations from Curiosity, tailored for Class 7 in Science.
This one-pager compiles key formulas and equations from the The Ever-Evolving World of Science chapter of Curiosity. 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
E = mc²
E represents energy (in joules), m is mass (in kg), and c is the speed of light (≈ 3 × 10⁸ m/s). This formula shows how mass can be converted into energy, a foundational idea in Einstein’s theory of relativity.
F = ma
F is force (in newtons), m is mass (in kg), and a is acceleration (in m/s²). This formula relates force, mass, and acceleration, revealing how acceleration depends directly on the net force acting on an object.
pH = -log[H⁺]
pH indicates the acidity or alkalinity of a solution, where [H⁺] is the concentration of hydrogen ions (mol/L). It is used to characterize solutions in chemistry and biology.
PV = nRT
P is pressure (in atm), V is volume (in L), n is the number of moles of gas, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T is temperature (in K). This equation describes the behavior of gases.
Q = mcΔT
Q is heat energy (in joules), m is mass (in kg), c is specific heat capacity (in J/(kg·K)), and ΔT is the change in temperature (in K). It calculates the heat transfer during temperature changes.
A = l × w
A is the area (in m²), l is length (in m), and w is width (in m). This formula is used to find the area of rectangles, useful in various real-world applications.
V = l × w × h
V is volume (in m³), l is length (in m), w is width (in m), and h is height (in m). This calculates the volume of rectangular prisms, which is essential in construction and storage.
N = n × Nₐ
N is the number of particles, n is the number of moles, and Nₐ is Avogadro's number (approximately 6.022 × 10²³ mol⁻¹). This formula connects moles to particles in chemistry.
s = ut + (1/2)at²
s is displacement, u is initial velocity, a is acceleration, and t is time. This kinematic equation describes motion, essential for understanding the concept of acceleration.
d = rt
d is distance (in km or m), r is rate (speed in km/h or m/s), and t is time (in hours or seconds). This formula describes motion and is frequently used in travel calculations.
Equations
Ohm’s Law: V = IR
V is voltage (volts), I is current (amperes), and R is resistance (ohms). It defines the relationship between current and voltage in a conductor. Useful for circuit-based questions.
Newton's Second Law: F = ma
F is the net force acting on the object (in newtons), m is the mass of the object (in kg), and a is the acceleration produced (in m/s²). This law is fundamental for understanding motion.
Conservation of Mass: m_initial = m_final
This principle states that in a closed system, the total mass remains constant over time, meaning mass is neither created nor destroyed in chemical reactions.
Chemical Reaction Rate: Rate = k[A]^m[B]^n
This equation describes how the rate of a chemical reaction depends on the concentration of reactants [A] and [B], with k being the rate constant and m, n being the reaction orders.
Work done: W = Fd cos(θ)
W is work done (in joules), F is force applied (in newtons), d is distance moved (in meters), and θ is the angle between the force and displacement direction.
Density: ρ = m/V
ρ is density (in kg/m³), m is mass (in kg), and V is volume (in m³). Density is a key property of materials, assisting in the identification of substances.
Kinetic Energy: KE = (1/2)mv²
KE is kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). It quantifies the energy of an object in motion and is crucial in mechanics.
Potential Energy: PE = mgh
PE is potential energy (in joules), m is mass (in kg), g is acceleration due to gravity (≈ 9.81 m/s²), and h is height (in meters). This formula helps in understanding energy storage.
Speed = distance/time
Speed is a measure of how fast an object is moving, calculated as distance covered over time taken, and is fundamental in various fields of study.
Pressure: P = F/A
P is pressure (in pascals), F is force (in newtons), and A is area (in m²). This formula describes how force is distributed over an area, commonly used in fluid mechanics.
