Question

Hot milk in a cup is to be drunk $5minutes$ after pouring. When should the sugar be mixed in it in order that it remains hot at the time of drinking?

• A. just after pouring
• B. at the time of drinking
• C. at any time
• D. after some milk is taken

Answer 1

Answer: (A)

just after pouring

Assume that in 5 minutes a heat of Q flows out of the cup of tea:
If we add sugar at the beginning:
$Q=(m_{tea}{c}_{tea}+m_{sugar}{c}_{sugar})\Delta T$
$\Delta T=\frac{Q}{(m_{tea}{c}_{tea}+m_{sugar}{c}_{sugar})}$
If we add sugar at the end:
$Q=\left(m_{tea}{c}_{tea}\right)\Delta T$
$\Delta T=\frac{Q}{\left(m_{tea}{c}_{tea}\right)}$
As we can see in the first case $\Delta T$ is smaller and hence the tea would remain hotter if we added sugar at the start.