• Pixel-art sticker of Paddlo, personifying Mechanical Equivalent of Heat, with the caption “Stir It Hard, Warm It Up.”

IndexHeat & EntropySticker

Paddlo

Mechanical Equivalent of Heat Physics

\[W = m c \Delta T\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Paddlo, a paddle wheel who warms water just by stirring it. In the 1840s James Joule showed work and heat are equivalent. A 10 kg weight falling 2 m does about 196 J of work, warming 1 kg of water by only about 0.05 K. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Paddlo, a paddle wheel who warms water just by stirring it.

In the 1840s James Joule set out to show that heat and work are two forms of the same thing. He hung weights on strings wound around a spindle. As the weights fell, they spun paddles inside an insulated tank of water, and the churning water became very slightly warmer.

The work done by the falling weights equals the heat gained by the water, W = mcΔT. A 10 kg weight falling 2 m does about 10 × 9.81 × 2 ≈ 196 J of work. Spread through 1 kg of water, with c = 4186 J/(kg·K), it raises the temperature by only about 0.05 K.

Joule needed very careful thermometers and many repeated drops to see such small changes.

His result that a fixed amount of work always gives the same amount of heat helped establish the conservation of energy, and the SI unit of energy, the joule, is named after him.

Equations

\[W = m c \Delta T\]
Symbols
SymbolMeaningUnit
\(W\) work done on the water \(\mathrm{J}\)
\(m\) mass of the water \(\mathrm{kg}\)
\(c\) specific heat capacity of water \(\mathrm{J/(kg·K)}\)
\(\Delta T\) rise in temperature \(\mathrm{K}\)