# the tempreature of 600g of cold water rises by15celcius when 300g of hot water at 50 celcius is added to it. What was the initial tempreature of the cold water. this Q based on calorimetery

jeew-m | Certified Educator

Here we mix cold water with hot water. So what happen at mixing is cold water absorbs heat from hot water and increase its temperature. Due to this hot water loss its energy and temperature will come down. At one stage this system will come to a neutral position where no heat transfer will occur and the temperature of the system is constant.

Let us say;

`theta_1` = initial temperature of cold water

`theta_2` = final temperature of the system

But according to the data in the question;

`theta_2` = `theta_1` +15

We know heat absorbed or loss by and object can be written as,

`Q = M*C*theta`

Where;

Q = heat loss or heat gain by the object

M = mass of the object

C = specific heat capacity of water

`theta` = temperature difference

Heat absorbed by cold water = 600*C*( `theta_2- theta_1` )

= 600*C*( `theta_1+15- theta_1` )

= 600*15*C

Heat loss by hot water          = 300*C*(50- `theta_2` )

= 300*C*(50- (`theta_1+15` ))

= 300*C*(35- `theta_1` )

Heat absorbed by cold water = heat loss by hot water

`600*15*C = 300*C*(35- theta_1)`

`theta_1 = 5`

So the initial temperature of cold water is 5C