Let the optimum volume of hot water or oil taken in the hot water bag be #V# and #d# represents the density of the liquid taken, If #Deltat# be the rate of fall of temperature of the liquid per sec due to transmission of heat at the rate #H# during its use .
Then we can write
#VdsDeltat=H#, where #s# is the specific heat of liquid taken in the bag,
So #Deltat=H/(Vds)#
This equation suggests that the fall of temperature #Delta# is inversely proportional to the product #ds# when H and V remaining more or less same.
The product of density #(d)# and specific heat #(s)# for oil is much less than that of water . This means the rate of fall of temperature of hot liquid in the bag becomes higher in case of oil, So the hot bag becomes useless quickly as it fails to give required warmth for a considerable period of time if oil is used instead of water in the water bag.
