Answer:
The required relation is,
[tex]\frac {dV}{dt}[/tex] = [tex]c{\frac{dT}{dt}}[/tex]
Step-by-step explanation:
We know that for a certain amount of dry gas when the pressure is kept constant it's volume V and temperature T is related by the function,
V = cT -----------------------(1) [where "c" is a constant]
So, in that case rate of change of volume(V) with respect to time (t),
= [tex]\frac {dV}{dt}[/tex]
will be equal to ,
[tex]c{\frac{dT}{dt}}[/tex]
where [tex]\frac {dT}{dt}[/tex] is equal to rate of change of temperature (T) with respect to time (t) and c is the constant stated before.
So, the required relation is,
[tex]\frac {dV}{dt}[/tex] = [tex]c{\frac{dT}{dt}}[/tex]
