The resistance wire of a 1200 W hair dryer is 80 cm long and has a diameter of 0⋅3 cm. What is the rate of heat generation in the wire per unit volume?

Concept:-

The rate of heat generation in the wire per unit volume is given by,

\(Q_{gv} = \frac{Rating}{Volume \;of\;resistance\;wire}\;\)

Calculation:

Given:

Rating = 1200 W

Length = 80 cm

Diameter = 0.3 cm

Now on putting all the values in the formula,

→ \(Q_{gv} = \frac{Rating}{Volume \;of\;resistance\;wire}\;\)

The volume of the cylindrical resistance wire is,

V = πD²L/4

Volume = \( V = \frac{\pi 0.3^2\times 80}{4}\;\) 

Volume = 5.655 cm³

Heat generation in the wire per unit wire is,

⇒ \(Q_{gv} = \frac{1200}{5.655} = 212.206\;~\) W/cm³