Question

Three identical silver cups A, B, and C contain three liquids of same densities at same temperature higher than the temperature of the surrounding. If the ratio of their specific heat capacities is 1:2:4, then

• A. A cools faster than B but slower than C
• B. B cools faster than B but slower than A
• C. A cools faster than B and C
• D. C cools faster than B and A
• E. B cools faster than A and C

Answer 1

The Correct Option is B, C

The rate of cooling of a liquid depends on its specific heat capacity. The liquid with a smaller specific heat capacity will lose heat faster. In this case, the ratio of specific heat capacities is 1 : 2 : 4 for liquids A, B, and C, respectively.
Liquid A has the smallest specific heat capacity, so it cools the fastest.
Liquid B has a medium specific heat capacity, so it cools slower than A but faster than C.
Liquid C has the largest specific heat capacity, so it cools the slowest. Thus, the correct answer is that B cools faster than C but slower than A.

The correct option is (B) : B cools faster than B but slower than A and (C): A cools faster than B and C

Answer 2

The rate of cooling is governed by Newton's law of cooling, but the time taken to cool depends on the heat capacity of the liquid.  

Heat content of a body is: $$ Q = mc\Delta T $$ where \( m \) = mass (same for all, since density and volume are same), \( c \) = specific heat capacity, \( \Delta T \) = temperature difference. 

Given the ratio of specific heats: $$ c_A : c_B : c_C = 1 : 2 : 4 $$ 
So, for the same initial temperature difference, more specific heat means more energy to lose → slower cooling. 

B cools faster than B but slower than A and (C): A cools faster than B and C