Question
Cold milk enters a small sterilizing unit and flows over an electrical heating element.
The temperature of the milk is raised from 11°C to 84°C. A mass of 55g of milk enters
the sterilizing unit every second.
Specific heat capacity of milk = 3.9kJkg-1K-1
(a) Estimate the power input to the heating element. State an appropriate unit
for your answer. [2]
(b) Outline whether your answer to (a) is likely to overestimate or underestimate
the power input. [2]
(c) Discuss, with reference to the molecules in the liquid, the difference between milk
at 11°C and milk at 84°C. [2]
(d) The milk flows out through an insulated metal pipe. The pipe is at a temperature
of 84°C. A small section of the insulation has been removed from around the pipe.
(i) State how energy is transferred from the inside of the metal pipe to the outside
of the metal pipe. [1]
(ii) The missing section of insulation is 0.56m long and the external radius of the
pipe is 0.067m. The emissivity of the pipe surface is 0.40. Determine the energy
lost every second from the pipe surface. Ignore any absorption of radiation by
the pipe surface. [3]
(iii) Describe one other method by which significant amounts of energy can be
transferred from the pipe to the surroundings. [2]
Answer/Explanation
Ans.
(a) energy required for milk entering in $1 \mathrm{~s}=$ mass $x$ specific heat $x 73 \sqrt{ }$ $16 \mathrm{~kW}$ OR $16000 \mathrm{~W} \checkmark$
(b) Underestimate / more energy or power required $\checkmark$
because energy transferred as heat / thermal energy is lost «to surroundings or electrical components» $\checkmark$
(c) the temperature has increased so the internal energy / ” average $» \mathrm{KE}$ «of the molecules» has increased $O R$ temperature is proportional to average KE “of the molecules».
«therefore» the “average» speed of the molecules or particles is higher OR more frequent collisions ” between molecules “OR spacing between molecules has increased $O R$ average force of collisions is higher $O R$ intermolecular forces are less $O R$ intermolecular bonds break and reform at a higher rate $O R$ molecules are vibrating faster. $\checkmark$
(d) (i) conduction/conducting/conductor «through metal» $\checkmark$
(d) (ii) use of $P=e \sigma A T^4$ where $T=357 \mathrm{~K} \checkmark$
use of $A=2 \pi r I \ll=0.236 \mathrm{~m}^2 » \checkmark$
$P=87 \ll W » \checkmark$
(d) (iii) convection «is likely to be a significant loss» $\checkmark$
«due to reduction in density of air near pipe surface» hot air rises «and is replaced by cooler air from elsewhere “
OR
“due to” conduction “of heat or thermal energy” from pipe to air $\checkmark$