A 645 g piece of iron is plunged into 375 g of water. The temperature of the water increases from 26 C to 87 C. If the heat capacity of iron is 0.449 J/g C, what must have been the original temperature (in C) of the piece of iron

417 °C

Explanation:

From the question given above, the following data were obtained:

Mass of iron (Mᵢ) = 645 g

Specific heat capacity of iron (Cᵢ) = 0.449 J/gºC

Mass of water (Mᵥᵥ) = 375 g

Initial temperature of water (Tᵥᵥ) = 26 °C

Equilibrium temperature (Tₑ) = 87 °C

Specific heat capacity of water (Cᵥᵥ) = 4.184 J/gºC

Initial temperature of iron (Tᵢ) =?

The initial temperature of iron can be obtained as follow:

Heat lost by iron = heat gain by water

MᵢCᵢ(Tᵢ – Tₑ) = MᵥᵥCᵥᵥ(Tₑ – Tᵥᵥ)

645 × 0.449(Tᵢ – 87) = 375 × 4.184 (87 –26)

289.605(Tᵢ – 87) = 1569 × 61

289.605Tᵢ – 25195.635 = 95709

Collect like terms

289.605Tᵢ = 95709 + 25195.635

289.605Tᵢ = 120904.635

Divide both side by 289.605

Tᵢ = 120904.635 / 289.605

Tᵢ ≈ 417 °C

Thus, the original temperature of the iron is 417 °C

Sound waves travel faster in a liquid than a gas, our ears are just not designed to  translate the faster moving waves.

Explanation:

Sound waves are mechanical waves which travel through vibrating the medium (the "stuff") they're traveling through. This means they actually move faster through materials that are more dense, and will move more quickly through liquid than gas, and a solid than a liquid. However, our ears are adapted to "translating" sound waves in air rather than water, so we don't understand the music well when the waves move through the water.

A similar idea explains why our vision is blurry underwater; light waves travel at a different speed (slower, not faster!) in water and our eyes perceive this change in speed as blurriness.