Question

The burner on an electric stove has a power output of 2.0 kW. A 750 g stainless steel teakettle is filled with 20°C water and placed on the already hot burner. If it takes 3.0 min for the water to reach a boil, what volume of water, in cm3, was in the kettle? Stainless steel is mostly iron, so you can assume its specific heat is that of iron.

Short answer

The volume of the cubic is $994c{m}^3$

Step-by-step solution

Definition of unitary efficiency 

Unitary efficiency defines that no loss will be seen due to the change of variables.

Finding teh volume of cubic 

The haet equation is Q=Pt

$m_k,m_w,c_{i,}{c}_w$are the mass of the kettle, the mass of water, specific heat in the kettle and specific heat in the water.

$Q=∆T(c_i{m}_k+c_w{m}_w)$

role="math" localid="1649148289466" $\begin{array}{rcl}{m}_w& =& pV\\ Q& =& Pt\\ Q& =& ∆T(c_i{m}_k+c_w{m}_w)\end{array}$

Applying all values

$\begin{array}{rcl}V& =& \frac{1}{c_w\rho }(\frac{P}{(∆T)}-c_i{m}_k)\\ V& =& \frac{1}{4190\times 1000}(\frac{2000\times 3\times 60}{(100-20)}-449\times 0.75)=994c{m}^3\end{array}$