Question

You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 20 mm $\times$1.5 mm rectangular cross section, and the distance from the boiling water to your 35°C hand is 18 cm. How long does it take the spoon to transfer 25 J of energy to your hand?

Short answer

It can take 5.8 s long for the spoon to transfer 25 J of energy

Step-by-step solution

Description of the provided information 

As per the provided information

The copper spoon has a 20 mm $\times$1.5 mm rectangular cross section, and the distance from the boiling water to 35°C hand is 18 cm.

Result 

For thermal conduction:

$\frac{dQ}{dt}=\frac{kA}{L}∆T$

In this case, dQ= heat and dt= time.

In case of time is large, localid="1649152723690" $\frac{Q}{t}=\frac{kab}{L}∆T$

Therefore on the basis of numerics and the formula for rectangle area,

localid="1649152719287" $$\begin{gathered} t=\frac{QL}{kab∆T} \\ =\frac{25·0.18}{400·0.02·0.0015·(100-35)} \\ =5.8s \end{gathered}$$

Therefore, it can take 5.8s long for the spoon to transfer 25 J of energy.