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Topic 19 of 19

Temperature, Heat & Thermodynamics

Thermodynamics describes energy at the macroscopic level — temperature, heat, and work. It governs everything from the efficiency of engines to the flow of heat through a building. The fundamental laws place absolute limits on what any heat engine can achieve and define the direction of natural processes.

Key Concepts

Temperature Scales

Celsius (

°

C) and Kelvin (K) are related by

T_K = T_C + 273.15

. Kelvin is the SI unit; absolute zero (0 K) is the lowest possible temperature, where molecular motion is minimal.

Thermal Expansion

Most materials expand when heated. Linear expansion:

\Delta L = \alpha L_0 \Delta T

(α = coefficient of linear expansion). Volume expansion:

\Delta V = \beta V_0 \Delta T

where

\beta \approx 3\alpha

Ideal Gas Law

PV = nRT

relates pressure

P

, volume

V

, amount

n

(moles), and temperature

T

(in kelvin).

R = 8.314

J/(mol·K). The ideal gas is a good model for real gases at low pressure and high temperature.

Heat and Specific Heat

Heat

Q

is energy transferred due to a temperature difference.

Q = mc\Delta T

, where

c

is the specific heat capacity (J/kg·K). For phase changes:

Q = mL

(L = latent heat, no temperature change).

First Law of Thermodynamics

Energy conservation:

\Delta U = Q - W

. Internal energy

U

increases when heat flows in (

Q > 0

) and decreases when the system does work (

W > 0

). This is the most general statement of energy conservation.

Second Law of Thermodynamics

Heat flows spontaneously only from hot to cold. Entropy (disorder) of an isolated system never decreases. No heat engine operating between temperatures

T_H

and

T_C

can exceed the Carnot efficiency

\eta_\text{Carnot} = 1 - T_C/T_H

Key Equations

Ideal gas law

PV = nRT, \quad R = 8.314 \text{ J/(mol·K)}

T must be in kelvin. n is moles. Also written PV = NkT where N is molecule count and k = 1.38×10⁻²³ J/K.

Heat and specific heat

Q = mc\,\Delta T

c is the specific heat capacity of the material. For phase changes: Q = mL (no ΔT).

Thermal expansion

\Delta L = \alpha L_0\,\Delta T, \quad \Delta V = \beta V_0\,\Delta T

α ≈ 10⁻⁵ to 10⁻⁶ K⁻¹ for most solids; β ≈ 3α.

First law of thermodynamics

\Delta U = Q - W

ΔU = change in internal energy; Q = heat added to system; W = work done by system.

Carnot (maximum) efficiency

\eta_\text{Carnot} = 1 - \frac{T_C}{T_H}

T in kelvin. No real engine can exceed this; it requires reversible processes.

Worked Example

Heating Water — Heat Calculation

Problem

How much heat is required to raise 2 kg of water from 20°C to 100°C? ( $c_\text{water} = 4186$ J/kg·K.)

Solution

Q = mc\,\Delta T = 2\times4186\times(100-20)

Q = 2\times4186\times80 = 669{,}760 \text{ J} \approx 670 \text{ kJ}

Answer ≈ 670 kJ of heat required.

Practice

Exercises

7 problems

Free preview

2 free · 5 Pro

Exercise 1 / 7 Free

+10 XP

An ideal gas at P₁ = 100 kPa, V₁ = 4 L is compressed isothermally to V₂ = 2 L. Watch the pressure bar change. Find P₂ using Boyle's law: P₁V₁ = P₂V₂.

V = 4.0 L

P₂ (at V=2L) = kPa

Exercise 2 / 7 Free

+10 XP

The P-V diagram shows an isobaric expansion at P = 200 kPa from V₁ = 2 L to V₂ = 4 L. Drag the handle to see the shaded work area. Find W = PΔV.

W = J

3 of 7

An ideal gas in a piston has $n = 2$ mol, $T = 300$ K, and pressure $P = 1.5\times10^5$ Pa. What is the volume (in L)? Use $R = 8.314$ J/(mol·K). (1 m³ = 1000 L.)

Unlock Exercise 3