Question

A) A common practice for a person with a high fever is to take a bath in cool water. Assuming an 80 kg person is really ill and needs to cool down from 40°C to 37°C. What is the minimum amount of water needed for bathing assuming the water begins at room temperature, 25°C? The specific heat of the body on average is 3470 J/kg°C and water is 4186 J/kg°C. 17.

b) Students want to impress their physics teacher by writing an essay which describes the heating of ice at a temperature below 0°C to steam at a temperature above 100°C. Write such a paragraph using the terms energy, temperature, and phase change. Be sure to include a description of the five major stages.

Answer 1

A) heat gained by water = heat lost by body

let mass of water = M

Therefore,

M c_{​​​​​​w} ∆T = m × C_{​​​​​​b} ∆t

M × 4186 × ( 37- 25) = - 80×3470×(37-40)

M× 50232 = 832800

M = 16.58 kg

Therefore, 16.58 kg of water or 16580 ml of water is required.

B) let initial temperature of ice is x degree Celsius ; X<0°C

Step 1 : the ice is heated from x ° C to 0°C by providing heat equal to mass of ice×specific heat capacity of ice×(0-x)

Step 2 : the ice at 0 °C is further heated to change its state from solid to liquid by providing heat equal to latent heat of fusion i e. = Mass of ice×latent heat of fusion.

In this phase change, the temperature remains constant till all the ice at 0°C is converted into water at 0°C

Step 3 : the water at 0 °C is heated to raise its temperature from 0°C to 100°C , by oroprovid heat equals to mass of water × specific heat of water × (100-0)

Step 4 : the water at 100 °C is further heated to change its state from liquid to gas by providing heat equal to latent heat of vapourisation i e. = Mass of water×latent heat of vapourisation.

In this phase change, the temperature remains constant till all the water at 100°C is converted into steam at 100°C .

Step 5: lastly, the steam at 100°C is heated further to raise its temperature to some y°C by providing heat equals to mass of steam × specific heat capacity of steam × (y-100)