Question

A bottle of water with mass 0.9 kg is left out in the sun, the radiation from the sun warms up the water bottle. If the water bottle was initially 10°C and the sun provided 120,000 J of thermal energy, calculate the final temperature of the water. Use C = 4182 j/kgK for the specific heat of water.

Answer 1

Final temperature, T2 = 314.9 Kelvin

Step-by-step explanation:

Given the following data:

Mass = 0.9kg

Initial temperature, T1 = 10°C to Kelvin = 10 + 273 = 283K

Quantity of heat = 120,000 J

Specific heat capacity = 4182 j/kgK

To find the final temperature;

Heat capacity is given by the formula;

`Q = mcdt`

Where;

Q represents the heat capacity or quantity of heat.

m represents the mass of an object.

c represents the specific heat capacity of water.

dt represents the change in temperature.

Making dt the subject of formula, we have;

`dt = \frac {Q}{mc}`

Substituting into the equation, we have;

`dt = \frac {120000}{0.9*4182}`

`dt = \frac {120000}{3763.8}`

dt = 31.9K

Now, the final temperature T2 is;

But, dt = T2 - T1

T2 = dt + T1

T2 = 31.9 + 283

T2 = 314.9 Kelvin