A container is filled up to the brim with 500 g of water and 1000 g of mercury. When 21200 cal of heat is supplied to the system, 3.52 g of water flows out of the container. Neglecting the expansion of the container, find the coefficient of real expansion of mercury. Given, volume expansion coefficient of water =1.5 times 10^(-4@)C^(-1), density of mercury =13.6g*cm^(-3), density of water 1g*cm^(-3) and specific heat capacity of mercury =0.03cal*g^(-1)*""^(@)C^(-1).

A container is filled up to the brim with 500 g of water and 1000 g of

1.	A container is filled up to the brim with 500 g of water and 1000 g of mercury. When 21200 cal of heat is supplied to the system, 3.52 g of water flows out of the container. Neglecting the expansion of the container, find the coefficient of real expansion of mercury. Given, volume expansion coefficient of water =1.5 times 10^(-4@)C^(-1), density of mercury =13.6gcm^(-3), density of water 1gcm^(-3) and specific heat capacity of mercury =0.03calg^(-1)""^(@)C^(-1).
Answer» Solution :Due to the application of heat, 3.52 g i.e., 3.52 `cm^(3)` of WATER flows out of the container. `therefore` The TOTAL expansion of MERCURY and water `=3.52cm^(3).` Let the rise in temperature `=t^(@)C.` Heat absorbed by mercury + heat absorbed by water = 21200 `therefore "" 500 times 1 times t+1000 times 0.03 times t=21200 " or, " t=40^(@)C` `therefore` Expansion of water `=500 times 1.5 times 10^(-4) times 40=3 cm^(3)` `therefore` Expansion of mercury `=(3.52-3)=0.52 cm^(3)` `therefore ""1000/13.6 times gamma times 40=0.52` `""[gamma=` volume expansion COEFFICIENT of mercury`]` `therefore "" gamma=1.768 times 10^(-4@)C^(-1).`