FIG. $9\mathrm{.}3p-v$ and $T-s$ diagrams of the air$-$standard Otto cycle

Relating states of equal specific entropy: $s=0$ :

Constant Specific Heats

$\frac{T_2}{T_1}=(\frac{p_2}{p_1}{)}^{\frac{k-1}{k}}$

$\frac{T_2}{T_1}=(\frac{v_1}{v_2}{)}^{k-1}$

$\frac{p_2}{p_1}=(\frac{v_1}{v_2}{)}^k$

where $k=\frac{c_p}{c_v}$ is given in Tables A$-20$

Variable Specific Heats $-$

$\frac{p_2}{p_1}=\frac{p_{r2}}{p_{r1}}(air$ only$)$

$\frac{v_2}{v_1}=\frac{v_{r2}}{v_{r1}}(air$ only$)$

where $p_r$ and $v_r$ are provided

in Tables A$-22.$