Answer : The initial temperature of the limestone is
.
Solution : Given,
Mass of limestone = 62.6 g
Mass of water = 75 g
Final temperature of limestone = 
Final temperature of water = 
Initial temperature of water = 
The specific heat capacity of limestone = 
The specific heat capacity of water = 
The formula used :
q = m × c × ΔT
where,
q = heat required
m = mass of an element
c = heat capacity
ΔT = change in temperature
According to this, the energy as heat lost by the system is equal to the gained by the surroundings.
Now the above formula converted and we get

![m_{system}\times c_{system}\times (T_{final}-T_{initial})_{system}= -[m_{surrounding}\times c_{surrounding}\times (T_{final}-T_{initial})_{surrounding}]](https://tex.z-dn.net/?f=m_%7Bsystem%7D%5Ctimes%20c_%7Bsystem%7D%5Ctimes%20%28T_%7Bfinal%7D-T_%7Binitial%7D%29_%7Bsystem%7D%3D%20-%5Bm_%7Bsurrounding%7D%5Ctimes%20c_%7Bsurrounding%7D%5Ctimes%20%28T_%7Bfinal%7D-T_%7Binitial%7D%29_%7Bsurrounding%7D%5D)
![m_{limestone}\times c_{limestone}\times (T_{final}-T_{initial})_{limestone}= -[m_{water}\times c_{water}\times (T_{final}-T_{initial})_{water}]](https://tex.z-dn.net/?f=m_%7Blimestone%7D%5Ctimes%20c_%7Blimestone%7D%5Ctimes%20%28T_%7Bfinal%7D-T_%7Binitial%7D%29_%7Blimestone%7D%3D%20-%5Bm_%7Bwater%7D%5Ctimes%20c_%7Bwater%7D%5Ctimes%20%28T_%7Bfinal%7D-T_%7Binitial%7D%29_%7Bwater%7D%5D)
Now put all the given values in this formula, we get
![62.6g\times 0.921J/g^{0}C \times (51.9^{0}C-T_{\text{ initial limestone}})= -[75g\times 4.186J/g^{0}C \times (51.9^{0}C-23.1^oC)]](https://tex.z-dn.net/?f=62.6g%5Ctimes%200.921J%2Fg%5E%7B0%7DC%20%5Ctimes%20%2851.9%5E%7B0%7DC-T_%7B%5Ctext%7B%20initial%20limestone%7D%7D%29%3D%20-%5B75g%5Ctimes%204.186J%2Fg%5E%7B0%7DC%20%5Ctimes%20%2851.9%5E%7B0%7DC-23.1%5EoC%29%5D)
By rearranging the terms, we get the value of initial temperature of limestone.

Therefore, the initial temperature of the limestone is
.