Thermodynamics

$$\nu =\frac{V}{V_{\mu}}=\frac{m}{\mu}=\frac{N}{N_A}$$

$$P=NkT$$

$$PV=\nu RT$$

$$v_t=\sqrt{\frac{3RT}{\mu}}$$

$$P_1=P_0+\rho gh$$

Monoatomic gas

$$C_V=\frac{3}{2}R$$

$$C_P=\frac{5}{2}R$$

Diatomic gas

$$C_V=\frac{5}{2}R$$

$$C_P=\frac{7}{2}R$$

Poliatomic gas

$$C_V=3R$$

$$C_P=4R$$

$$\Delta U=Q-L$$

$$U=\nu C_VT$$

Isochoric process

$$V=ct \quad L=0 \quad \frac{P}{T}=ct \quad \Delta U=Q$$

Isobaric process

$$P=ct \quad L=p\Delta V \quad \frac{V}{T}=ct \quad Q=\nu C_p\Delta T$$

Isothermal process

$$T=ct \quad L=Q=\nu RT \ln \frac{V_f}{V_i} \quad \Delta U=0 \quad PV=ct$$

Adiabatic process

$$Q=0 \quad \Delta U=-L \quad PV^{\gamma}=ct$$

Politropic process

$$PV^n=ct \quad L=-\nu \frac{R}{n-1}\Delta T \quad C=C_V-\frac{R}{n-1}$$

$$Q=c\Delta T=c_m m \Delta T= C_{\mu} \nu \Delta T$$

$$\gamma =\frac{E}{\rho}$$

E-Young modulus

$$\eta =\frac{L}{Q_p}=1-\frac{|Q_c|}{Q_p}$$

Carnot Cycle

$$\eta_c=1-\frac{T_{min}}{T_{max}}$$

Otto cycle

$$\eta_o=1-\frac{1}{\epsilon^{\gamma-1}}$$

$$\epsilon=\frac{V_1}{V_2}$$

Diesel cycle

$$\eta_d=1-\frac{\alpha^{\gamma}-1}{\gamma \epsilon^{\gamma}(\alpha-1)}$$

$$\epsilon=\frac{V_1}{V_2} \quad \alpha=\frac{V_3}{V_2}$$

$$Q_tr=m\lambda_{tr}$$

$$\lambda_{tr}$$ - specific latent heat

Andrews Isothermes



$$t^o(F)=\frac{9}{5}t^o(C)+32^o$$