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}}

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Siujoeng Lau

Liberty will never perish.

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