List of formulas related to Thermodynamics
The First Law Of Thermodynamics
ΔU: change in internal energy, W: work done by the system, Q: heat added into or out of the system
$$ \Delta U = W + Q $$Application Of First Law To Ideal Gas Laws
Volume is constant
$$ \Delta V = 0 => W = 0 $$ $$ => Q = \Delta U $$
Pressure is constant, W’: work created by gas
$$ \Delta V \neq 0 => W \neq 0 $$ $$ => Q = \Delta U - W $$ $$ W = -W' = p_1(V_2 - V_2) $$ $$ => Q = \Delta U + W' $$
Temperature is constant
$$ t = costant => \Delta U = 0 $$ $$ => Q = \Delta U - W = -W(W \neq 0) $$
The Second Law Of Thermodynamics
The efficiency of a cyclic heat engine
W’: work carried out per cycle(J), Q1: heat absorbed per cycle from the higher temperature(J), Q2’: heat rejected per cycle to the lower temperature(J)
$$ H = \frac{W'}{Q_1} $$ $$ W' = Q_1 - Q_2') $$ $$ => H = \frac{W'}{Q_1} = \frac{Q_1 - Q_2'}{Q_1} $$Maximum thermal efficiency
T1,T2: higher and lower temperatures
$$ H_{max} = \frac{T_1 - T_2}{T_1} $$