Answer : The final temperature of the mixture is ![22.7^oC](https://tex.z-dn.net/?f=22.7%5EoC)
Explanation :
In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.
![q_1=-q_2](https://tex.z-dn.net/?f=q_1%3D-q_2)
![m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)](https://tex.z-dn.net/?f=m_1%5Ctimes%20c_1%5Ctimes%20%28T_f-T_1%29%3D-m_2%5Ctimes%20c_2%5Ctimes%20%28T_f-T_2%29)
And as we know that,
Mass = Density × Volume
Thus, the formula becomes,
![(\rho_1\times V_1)\times c_1\times (T_f-T_1)=-(\rho_2\times V_2)\times c_2\times (T_f-T_2)](https://tex.z-dn.net/?f=%28%5Crho_1%5Ctimes%20V_1%29%5Ctimes%20c_1%5Ctimes%20%28T_f-T_1%29%3D-%28%5Crho_2%5Ctimes%20V_2%29%5Ctimes%20c_2%5Ctimes%20%28T_f-T_2%29)
where,
= specific heat of ethanol = ![2.3J/g^oC](https://tex.z-dn.net/?f=2.3J%2Fg%5EoC)
= specific heat of water = ![4.18J/g^oC](https://tex.z-dn.net/?f=4.18J%2Fg%5EoC)
= mass of ethanol
= mass of water
= density of ethanol = 0.789 g/mL
= density of water = 1.0 g/mL
= volume of ethanol = 45.0 mL
= volume of water = 45.0 mL
= final temperature of mixture = ?
= initial temperature of ethanol = ![9.0^oC](https://tex.z-dn.net/?f=9.0%5EoC)
= initial temperature of water = ![28.6^oC](https://tex.z-dn.net/?f=28.6%5EoC)
Now put all the given values in the above formula, we get
![(0.789g/mL\times 45.0mL)\times (2.3J/g^oC)\times (T_f-9.0)^oC=-(1.0g/mL\times 45.0mL)\times 4.18J/g^oC\times (T_f-28.6)^oC](https://tex.z-dn.net/?f=%280.789g%2FmL%5Ctimes%2045.0mL%29%5Ctimes%20%282.3J%2Fg%5EoC%29%5Ctimes%20%28T_f-9.0%29%5EoC%3D-%281.0g%2FmL%5Ctimes%2045.0mL%29%5Ctimes%204.18J%2Fg%5EoC%5Ctimes%20%28T_f-28.6%29%5EoC)
![T_f=22.7^oC](https://tex.z-dn.net/?f=T_f%3D22.7%5EoC)
Therefore, the final temperature of the mixture is ![22.7^oC](https://tex.z-dn.net/?f=22.7%5EoC)