Question

A 90kg person jumps from a 30m tower into a tub of water with a volume of 5m3 initially at 20°C. Assuming that all of the work done by the person is converted into heat to the water, what is the final temperature of the water? It’s helpful to first find the work done by the person to the water tub and then the amount of heat equivalent to that work. Make sure you have the correct value for the mass of the water. Include units.

Answer 1

Answer:

T₂ = 20.06 ° C

Explanation:

Given

P = 90 kg,  T₁ = 20 ° C,  h = 30 m,  c = 1.82 kJ / Kg * ° C

Using the formula to determine the final temperature of the water

T₂ = T₁ * P * h / Eₐ * c

The work done of the person to the water

Eₐ = 1000 kg / m³ * 5 m³ * 9.8 m / s²

Eₐ = 49000 N

T₂ = 20 ° C +[ (90 kg * 30m) / (49000 N * 1.82) ]

T₂ = 20.06 ° C