Unit 1: Quantities, Energy and Power

Physical Quantities, Standards and Units

Physical Quantities

A physical quantity is any property of a material or system that can be quantified by measurement. It is expressed as the combination of a numerical value and a unit.

Example: Length = 5 metres (5 is the numerical value, metres is the unit).

There are two main types of physical quantities:

1. Fundamental (or Base) Quantities: These are the basic quantities that are independent of each other. They are not defined in terms of other quantities.
2. Derived Quantities: These are quantities that are formed by combining fundamental quantities through multiplication or division.
   • Example: Speed = Length / Time
   • Example: Force = Mass × (Length / Time²)

Standards and Units

A unit is a specific, agreed-upon "standard" amount of a physical quantity, used to measure other amounts of the same quantity. For a unit to be useful, it must be:

• Well-defined: Everyone agrees on its exact definition.
• Accessible: It should be reproducible.
• Invariable: It should not change over time or with location.

A standard is the physical embodiment of a unit (e.g., the original platinum-iridium kilogram block in France was the *standard* for the *unit* "kilogram"). Modern standards are based on universal physical constants.

International System of Units (SI)

The SI (Système International d'Unités) is the modern form of the metric system and is the most widely used system of measurement. It is built upon seven base units corresponding to seven fundamental quantities.

Fundamental Quantity	SI Base Unit	Symbol
Length	Metre	m
Mass	Kilogram	kg
Time	Second	s
Electric Current	Ampere	A
Thermodynamic Temperature	Kelvin	K
Amount of Substance	Mole	mol
Luminous Intensity	Candela	cd

Standards of Time, Length and Mass

The definitions of the base units have evolved to become more precise, relying on fundamental constants of nature rather than physical objects.

• Standard of Time (The Second):
  The second (s) is defined by taking the fixed numerical value of the caesium frequency, Δν_Cs, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9,192,631,770 when expressed in the unit Hz, which is equal to s⁻¹. This is the principle behind atomic clocks.
• Standard of Length (The Metre):
  The metre (m) is defined by taking the fixed numerical value of the speed of light in vacuum (c) to be 299,792,458 when expressed in the unit m/s.
  This means 1 metre is the distance light travels in vacuum in 1/299,792,458 of a second.
• Standard of Mass (The Kilogram):
  The kilogram (kg) is defined by taking the fixed numerical value of the Planck constant (h) to be 6.62607015 × 10⁻³⁴ when expressed in the unit J·s, which is equal to kg·m²·s⁻¹. This definition is now based on a fundamental constant, replacing the old physical "Le Grand K" cylinder.

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Energy

Energy is defined as the capacity to do work.

It is a scalar quantity, and its SI unit is the Joule (J). (1 Joule = 1 Newton-metre)

Kinetic Energy (K)

Kinetic Energy is the energy an object possesses due to its motion.

K = (1/2) mv²

• `m` = mass of the object (in kg)
• `v` = speed of the object (in m/s)

If you double the mass of an object, you double its kinetic energy. But if you double the speed, you quadruple (2²) its kinetic energy. This is why high-speed car crashes are so much more destructive.

Potential Energy (U)

Potential Energy is stored energy an object possesses due to its position or configuration (its shape).

• Gravitational Potential Energy (U_g): Energy stored by an object due to its height in a gravitational field.

  U_g = mgh

  • `m` = mass (kg)
  • `g` = acceleration due to gravity (≈ 9.8 m/s²)
  • `h` = height (m) above a reference point
• Elastic Potential Energy (U_e): Energy stored in a stretched or compressed elastic object, like a spring or rubber band.

  U_e = (1/2) kx²

  • `k` = spring constant (in N/m)
  • `x` = displacement from the equilibrium (unstretched) position (m)

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Work and Power

Work (W)

In physics, work is done when a force (F) acts on an object, causing it to have a displacement (d) in the direction of the force.

W = F × d × cos(θ)

• `F` = magnitude of the force (in Newtons)
• `d` = magnitude of the displacement (in metres)
• `θ` = angle between the force and the displacement

The SI unit of work is the Joule (J). 1 J = 1 N·m.

Power (P)

Power is the rate at which work is done, or the rate at which energy is transferred.

P = W / t (Average Power)

• `W` = work done (in Joules)
• `t` = time taken (in seconds)

The SI unit of power is the Watt (W). 1 Watt = 1 Joule per second (1 J/s).

A common non-SI unit is horsepower (hp). 1 hp ≈ 746 W.

An alternative formula for instantaneous power is: P = F × v (Force × velocity).

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Conversion of Energy

This is the First Law of Thermodynamics, also known as the Principle of Conservation of Energy.

Energy cannot be created or destroyed; it can only be transformed from one form to another.

The total amount of energy in an isolated system remains constant.

Daily Life Examples:

• A falling ball: At the top, it has maximum Potential Energy (mgh). As it falls, `h` decreases (U decreases) and `v` increases (K increases). Its PE is converted into KE.
• A light bulb: Electrical energy is converted into light energy and heat energy (waste).
• A car: Chemical energy (in petrol) is converted by the engine into kinetic energy (motion) and heat energy (waste).
• A hydroelectric dam: Gravitational potential energy (of the water held high) is converted into kinetic energy (of the falling water), which turns a turbine (mechanical energy), which runs a generator to produce electrical energy.
• Photosynthesis: Radiant energy (sunlight) is converted by plants into chemical energy (sugars).

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Renewable and Non-Renewable Energy

Non-Renewable Energy

These are energy sources that are finite and cannot be replenished on a human timescale. They are "used up."

• Fossil Fuels (Coal, Oil, Natural Gas): Formed from the remains of dead plants and animals over millions of years.
  • Pros: High energy density, relatively cheap, established technology.
  • Cons: Produce greenhouse gases (like CO₂) when burned, causing global warming and climate change; cause air pollution (smog); finite supply.
• Nuclear Fuel (Uranium): Energy is released through nuclear fission.
  • Pros: Extremely high energy output, no greenhouse gas emissions.
  • Cons: Creates radioactive waste that is dangerous for thousands of years; risk of accidents (e.g., Chernobyl, Fukushima).

Renewable Energy

These are energy sources that are naturally replenished on a human timescale. They are "sustainable."

• Solar Energy: Energy from the sun's radiation.
  • Pros: Clean (no emissions), abundant, getting cheaper.
  • Cons: Intermittent (doesn't work at night), requires large land area.
• Wind Energy: Kinetic energy of moving air (wind) turns turbines.
  • Pros: Clean, no fuel cost.
  • Cons: Intermittent (needs wind), can be noisy, visual impact, potential danger to birds.
• Hydroelectric Energy: Potential energy of water stored in dams. (Already discussed).
  • Pros: Clean, reliable, can be stored and released on demand.
  • Cons: High initial cost, huge environmental impact (floods ecosystems, displaces people).
• Geothermal Energy: Heat energy from the Earth's interior.
  • Pros: Highly reliable, constant output.
  • Cons: Geographically limited to specific "hot spots."

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Heat Energy

Heat is a form of energy that is transferred between systems or objects with different temperatures. Heat is "energy in transit."

Temperature is a measure of the average kinetic energy of the molecules in a substance.

Heat energy always flows from a hotter object to a colder object until they reach thermal equilibrium.

Units of Heat Energy

• Joule (J): The SI unit of energy. Since heat is energy, its SI unit is the Joule.
• Calorie (cal): An older, common unit.

  1 calorie = the amount of heat energy required to raise the temperature of 1 gram of water by 1 degree Celsius.

• Food Calorie (Cal): This is actually a kilocalorie (kcal).
  1 Calorie = 1000 calories = 1 kcal

Conversion: 1 cal ≈ 4.184 J

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Energy Table, Flow, and Measurement

Energy Table and Discussions

This refers to comparing the energy content of various sources or the energy consumption of various activities. This provides context for "how much" energy we are talking about.

Energy Source / Activity	Approximate Energy (Joules)
Energy in 1 gram of sugar (1 food Cal)	~17,000 J (17 kJ)
Kinetic energy of a moving car (60 km/h)	~200,000 J (200 kJ)
Energy in 1 litre of petrol	~34,000,000 J (34 MJ)
Daily electricity use per home (India)	~30,000,000 J (30 MJ or 8.3 kWh)
Energy from 1 gram of Uranium-235	~82,000,000,000 J (82 GJ)

Energy Flow

An energy flow diagram (or Sankey diagram) is a visual way to show the conversion of energy. It illustrates the law of conservation of energy by showing all the outputs, including useful energy and wasted energy.

Example: Incandescent Light Bulb

• Input: 100% Electrical Energy
• Useful Output: ~5-10% Light Energy
• Wasted Output: ~90-95% Heat Energy

Measuring Energy

We don't usually measure energy directly; we measure other quantities and calculate it.

• Measuring Electrical Energy: Your home's electricity meter measures power (in kilowatts) and the time (in hours). It displays energy in kilowatt-hours (kWh).

  1 kWh = 1 kilowatt × 1 hour
  1 kWh = (1000 J/s) × (3600 s) = 3,600,000 J = 3.6 MJ

  This "unit" on your electricity bill is a unit of energy.
• Measuring Heat Energy: A calorimeter is used in a lab. It's an insulated container where a reaction takes place. By measuring the temperature change (ΔT) of a known mass (m) of water, we can calculate the heat absorbed or released using `Q = mcΔT` (where `c` is the specific heat capacity).

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Power Sources

This refers to the *source* that provides the energy to be converted. We have already discussed many of these in the "Renewable/Non-Renewable" section.

Common Daily Power Sources:

• Electrical Grid: This is our main "source." The grid itself is powered by a mix of primary sources:
  • Thermal (Coal, Natural Gas)
  • Hydroelectric (Dams)
  • Nuclear
  • Renewable (Solar, Wind)
• Batteries (Chemical Energy): Portable power sources that convert stored chemical energy into electrical energy via an electrochemical reaction.
  • Primary (Non-rechargeable): e.g., Alkaline batteries (for remotes). The reaction is one-way.
  • Secondary (Rechargeable): e.g., Lithium-ion batteries (in phones, laptops, electric cars). The reaction can be reversed by applying an external current.
• Internal Combustion Engine (Chemical Energy): Uses chemical energy from fuel (petrol, diesel) to produce mechanical power for vehicles.
• Solar Cells (Radiant Energy): Convert sunlight directly into electrical power. Used in calculators, satellites, and solar farms.
• Human Body (Chemical Energy): Your muscles convert chemical energy from food into mechanical power to walk, lift, or ride a bike. An average human can sustain about 100 Watts of power.