Solutions (^231)
whence
- n 2 1 - (T --- T 2 ) (T — T)-1.
2 ci
By hypothesis, 2 (T 1 — T) = T 1 — T 2 , and
hence T — T2 = T1 - T, and the ratio (T —2' 2 )1
(T 1 — T) = 1. Therefore,rni c2
nt2^ c1
i.e. the ratio of the masses of these liquids is in-
verse to the ratio of their specific heats.
2.27. In the former case, the water in the test tube
is mainly heated due to convection since warm
water is lighter than cold water. In the latter case,
water is cooled only as a result of heat exchange
between water layers in the test tube. Since the
conditions of heat exchange between the test tube
and outer water remain the same, t 1 < t 2.
It should be noted that if we change the param-
eters of the problem (20 °C -4- 0 °C and 80 °C
4 °C), we shall obtain a reverse answer. The reason
lies in the anomaly of water. In the temperature
interval from 0 to 4 °C, cold water is lighter than
warm water.
2.28. For the system under consideration (vessel-
water, vessel-water-ball), the heat flux per unit
time q = AQ/At through the surface of contact
with the ambient depends on the temperature
difference:AQ
At =aF (Tves—T),where t is the time, Tv„ is the temperature of the
vessel, T is the temperature of the ambient, and
F is a certain function of temperature. The coef-
ficient cc is determined by the conditions at the
contact of the system under consideration with
the ambient. In our case, the conditions at the
contact are identical for the two vessels, and hence
the coefficient cc is the same in both cases. The