# Temperature Differential

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Temperature differential, abbreviated as $$\Delta T$$ or TD, is the difference between two specific temperature points of a volume at a given time in a system.

### Temperature Differential Formula

$$\large{ \Delta T = T_h - T_l }$$

$$\large{ \Delta T = \frac{\dot {Q}_t \; l}{k_t} }$$     (heat transfer rate)

$$\large{ \Delta T = \frac {Q}{m \; c} }$$     (thermal energy)

$$\large{ \Delta T = \frac { \Delta l } { l_{ur} \; \alpha } }$$     (unrestrained pipe length)

Where:

$$\large{ \Delta T }$$ = temperature differential

$$\large{ \dot {Q}_t }$$ = heat transfer rate

$$\large{ l }$$ = length

$$\large{ m }$$ = mass

$$\large{ \Delta l }$$ = pipe length change due to temperature change

$$\large{ c }$$ = specific heat

$$\large{ T_h }$$ = high temperature

$$\large{ T_l }$$ = low temperature

$$\large{ k_t }$$ = thermal conductivity constant

$$\large{ Q }$$ = thermal energy

$$\large{ \alpha }$$  (Greel symbol alpha) = thermal expansion coefficient

$$\large{ l_{ur} }$$ = unrestrained pipe length