Question

A 100 mL sample of ethanol at 25°C is mixed with a 300 mL sample of ethanol at -5°C. The mixture is allowed to come to thermal equilibrium. What is the final temperature?

Answer 1

Answer: The final temperature of the mixture will be
`2.5^0C`

Step-by-step explanation:

`heat_(absorbed)=heat_(released)`

As we know that,

`Q=m* c* \Delta T=m* c* (T_(final)-T_(initial))`

`m_1* c_1* (T_(final)-T_1)=-[m_2* c_2* (T_(final)-T_2)]` .................(1)

where,

q = heat absorbed or released

`m_1` = mass of first sample of ethanol = 100 ml

`m_2` = mass of second sample of ethanol = 300 ml

`T_(final)` = final temperature = ?

`T_1` = temperature of first sample of ethanol =
`25^oC=298K`

`T_2` = temperature of second sample of ethanol =
`-5^oC=268K`

`c_1` =
`c_2` = specific heat of ethanol

Now put all the given values in equation (1), we get

`-100* (T_(final)-298)=[300* (T_(final)-268)]`

`T_(final)=275.5K=2.5^0C`

Therefore, the final temperature of the mixture will be
`2.5^0C`