Question

The heat current is written as deltaQ/Delta t.Why dont we write dQ/dt

Answer 1

delta technically means change, whereas dQ/dT is a derivative , I don't fully understand the a reason yet, but it's covered in multi-variate calculus.

But in short, delta just means change. dQ/dt = Lim deltaQ/deltaT as t-->0 It could also be said delta is average change over a period of time, dQ/dT is instantaneous change

Answer 2

What equation are you looking at that uses Deltas instead of differentials?

Answer 3

am just looking for the diferences..

Answer 4

Then yeah, what @DerBärJuden said, especially the limit part. If Q is a function of T, then the derivative of Q with respect to T is
\[\frac{\mathrm{d}Q(T)}{\mathrm{d} T} = \lim_{t \to 0} \ \frac{Q(T+t) - Q(T)}{(T+t)-T}=\lim_{t \to 0} \ \frac{Q(T+t) - Q(T)}{t} \]
as opposed to a similar expression using Deltas being
\[ \frac{ \Delta Q}{\Delta T} = \frac{Q_2-Q_1}{T_2-T_1}\]
Deltas are used primarily when there are substantive changes in each variable. The little d's are "differentials" of that variable - infinitesimal pieces of a continuous function; and
\[\frac{\mathrm{d}Q}{\mathrm{d} T}\]
is the instantaneous rate of change in Q with respect to T if Q is purely a function of T - if you're writing out full expressions, you can only use that notation generally if Q is purely in terms of T. Otherwise, you often use partial derivatives
\[\frac{\partial Q}{\partial T}\]
which means *exactly the same thing as a normal differential, except it indicate that Q is a function of multiple variables.

Answer 5

Perfect ! ;) :)