If, after some of the tea has been transferred to the thermos (as described in the passage), the teapot with its contents (at a temperature of 80 ∘ C ) was placed on the insulated warmer for 5 minutes, what would be the temperature at the end of this 5 minute period? (Assume that no significant heat transfer occurs with the surroundings)

If, after some of the tea has been transferred to the thermos (as described in t | TestHub

Passage / Comprehension

A $500 g$ teapot and an insulated thermos are in a $20^{\circ} C$ room. The teapot is filled with $1000 g$ of boiling water. 12 tea bags are then placed into the teapot. The brewed tea is allowed to cool to $80^{\circ} C$ , then $250 g$ of the tea is poured from the teapot into the thermos. The teapot is then kept on an insulated warmer that transfers $500 cal$ /min to the tea. Assume that the specific heat of brewed tea is the same as that of pure water, and that the tea bags have a very small mass compared to that of the water, and a negligible effect on the temperature. The specific heat of teapot is $0.17 J/g$ K and that of water is $4.18 J/g$ K. The entire procedure is done under atmospheric pressure. There are $4.18 J$ in one calorie.

If, after some of the tea has been transferred to the thermos (as described in the passage), the teapot with its contents (at a temperature of $80^{\circ} C$ ) was placed on the insulated warmer for 5 minutes, what would be the temperature at the end of this 5 minute period? (Assume that no significant heat transfer occurs with the surroundings)

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Answer:

Solution:

After pouring, $750 g$ of tea remains.
$Q = 500 (5) (4.18) = 10450 J$
$C = 750 (4.18) + 500 (0.17) = 3220 J/K$
$Δ T = \frac{10450}{3220} \approx 3.245 K$
$T_{f} \approx 83.2^{\circ} C$

Physics - Heat & Thermo Question with Solution | TestHub

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