A solid of mass $0.15 K g$ and at $100 ° C$ is placed in $0.25 K g$ of water, contained in a copper calorimeter of mass $0.12 K g$ , at $10 ° C$ . If the final temperature of the mixture is $20 ° C$ , calculate the sp. heat capacity of the solid.

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Solution

Step 1: Organised table of the given data
Substance Mass S.H.C Initial Temperature Final Temperature= $20 ° C$
Solid $150 g$ $?$ $100 ° C$ $θ_{F} = 100 - 20 = 80 ° C$
Liquid $250 g$ $4200 J g^{- 1} K^{- 1}$ $10 ° C$ $θ_{R} = 20 - 10 = 10 ° C$
Calorimeter $120 g$ $400 J g^{- 1} K^{- 1}$
Step 2: Calculating the heat energy
Let the specific heat capacity of the solid is $c$
The heat released by the solid is given as
$m c θ_{F} = 150 \times c \times 80$
The heat absorbed by the liquid is given as
$m c θ_{R} = 250 \times 4200 \times 10$
So,
the heat absorbed by the vessel $= m c θ_{R} = 120 \times 400 \times 10$
Step3: Calculating the thermal of the calorimeter
Heat released = Heat absorbed
$12000 c = 10500000 + 480000 12000 c = 10980000 c = \frac{10980000}{12000} c = 915 J g^{- 1} K^{- 1}$
Hence, the specific heat capacity of solid is $915 J K g^{- 1} K^{- 1}$

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Substance	Mass	S.H.C	Initial Temperature	Final Temperature= $20 ° C$
Solid	$150 g$	$?$	$100 ° C$	$θ_{F} = 100 - 20 = 80 ° C$
Liquid	$250 g$	$4200 J g^{- 1} K^{- 1}$	$10 ° C$	$θ_{R} = 20 - 10 = 10 ° C$
Calorimeter	$120 g$	$400 J g^{- 1} K^{- 1}$

A solid of mass 0.15Kg and at 100°C is placed in 0.25Kg of water, contained in a copper calorimeter of mass 0.12Kg, at 10°C. If the final temperature of the mixture is 20°C, calculate the sp. heat capacity of the solid.

A solid of mass $0.15 K g$ and at $100 ° C$ is placed in $0.25 K g$ of water, contained in a copper calorimeter of mass $0.12 K g$ , at $10 ° C$ . If the final temperature of the mixture is $20 ° C$ , calculate the sp. heat capacity of the solid.