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Standard X

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Early Conquests of Ranjit Singh

A piece of br...

Question

A piece of brass of mass $200 g$ at $100 ° C$ is placed in $400 g$ of turpentine oil, contained in a copper calorimeter of mass $50 g$ at $15 ° C$ . The final temperature of the mixture is $23 ° C$ . Find the specific heat capacity of turpentine oil.

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Solution

Step 1: Organised table of the given data
Substance Mass S.H.C Initial Temperature Final Temperature= $23 ° C$
Brass $200 g = \frac{200}{1000} k g$ $370 J K g^{- 1} K^{- 1}$ $100 ° C$ $θ_{F} = 100 - 23 = 77 ° C$
Oil $400 g = \frac{400}{1000} k g$ $?$ $15 ° C$ $θ_{R} = 23 - 15 = 8 ° C$
Calorimeter $50 g = \frac{50}{1000} k g$ $390 J K g^{- 1} K^{- 1}$ $15 ° C$
Step 2: Finding the specific heat capacity of turpentine oil
Let the specific heat capacity of the oil is $C_{t} .$
Heat gained by turpentine $+$ calorimeter $= [(\frac{400}{1000} \times C_{t}) + (\frac{50}{1000} \times C)] (23 - 15)$
$\begin{aligned} = (\frac{2}{5} C_{t} + \frac{1}{20} \times 390) \times 8 \\ = (\frac{2}{5} C_{t} + \frac{39}{2}) 8 \\ = (\frac{16}{5} C_{t} + 156) J \end{aligned}$
Now, heat loss of brass $= m c (d T)$
So, the heat lost is
$0.2 \times 370 \times 77 ° = 5698 J$
Since, $Heat gained = Heat lost$
$\begin{aligned} \frac{16}{5} C_{t} + 156 = 5698 \\ \frac{16}{5} C_{t} = 5698 - 156 \end{aligned} \frac{16}{5} C_{t} = 5542 C_{t} = \frac{5542 \times 5}{16} C_{t} = 1731.8 {JKg}^{- 1} K^{- 1}$
Hence, the sp heat capacity of turpentine oil is $1731.8 {JKg}^{- 1} K^{- 1} .$

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Substance	Mass	S.H.C	Initial Temperature	Final Temperature= $23 ° C$
Brass	$200 g = \frac{200}{1000} k g$	$370 J K g^{- 1} K^{- 1}$	$100 ° C$	$θ_{F} = 100 - 23 = 77 ° C$
Oil	$400 g = \frac{400}{1000} k g$	$?$	$15 ° C$	$θ_{R} = 23 - 15 = 8 ° C$
Calorimeter	$50 g = \frac{50}{1000} k g$	$390 J K g^{- 1} K^{- 1}$	$15 ° C$

A piece of brass of mass 200g at 100°C is placed in 400g of turpentine oil, contained in a copper calorimeter of mass 50g at15°C. The final temperature of the mixture is23°C. Find the specific heat capacity of turpentine oil.

A piece of brass of mass $200 g$ at $100 ° C$ is placed in $400 g$ of turpentine oil, contained in a copper calorimeter of mass $50 g$ at $15 ° C$ . The final temperature of the mixture is $23 ° C$ . Find the specific heat capacity of turpentine oil.