# Study Notes: SAT Physics Subject Test

## Heat and Thermodynamics

Temperature scales: $\small T(K)=T(^{\circ}C)+273$

Temperature change: $\small Q=mc \Delta T$ (c is the specific heat.)

Phase change: $\small Q=mL$ (L is the latent heat of transformation.)

#### Thermal expansion

$\small \Delta L = \alpha L_{0} \Delta T$ ($\small \alpha$ is the coefficient of linear expansion.)

$\small \Delta V = \beta V_{0} \Delta T$ ($\small \beta$ is the coefficient of volume expansion.)

#### The kinetic theory of gases

Pressure: $\small P = \frac{F}{A}$

The idea gas law: $\small PV=nRT$ (R is the universal gas constant.)

Translational kinetic energy: $\small K_{\text{avg}}=\frac{3}{2}k_{B}T$ ($\small k_{B}=1.38 \cdot 10^{-23} \cdot m^{2} \cdot kg \cdot s^{-2} \cdot K^{-1}$)

Velocity: $\small v_{\text{rms}}=\sqrt{\frac{3k_{B}T}{m}}=\sqrt{\frac{3RT}{M}}$

#### The laws of thermodynamics

• If object 1 and 2 are each in thermal equilibrium with object 3, then objects 1 and 2 are in thermal equilibrium with each other.
• Energy is neither created or destroyed in any thermodynamic system. ($\small W=P \Delta V$)
• The total amount of disorder (the total entropy) of a system plus its surroundings will never decrease.

efficiency of heat engines: $\small \text{efficiency}=\frac{\text{work output}}{\text{work input}} \cdot 100 \%$; $\small e=\frac{Q_{H}-|Q_{C}|}{Q_{H}}=1-\frac{|Q_{C}|}{Q_{H}}$

#### The Carnot Cycle

The most efficient heat engine follows what is known as the Carnot cycle.

For the Carnot cycle, efficiency ca nbe written as $\small e=\frac{T_{H}-T_{C}}{T_{H}}$