Question

- 75.0 gram sample of water at 25.0 degrees Celsius is mixed with a 100. gram sample of water at 60.0 degrees Celsius.

What is the final temperature of the water? (No units necessary in the answer)

Answer 1

45

Step-by-step explanation:

`m_1` = First sample mass of water =
`75\ \text{g}`

`\Delta T_1` = Change in temperature of the first sample of water =
`25-T`

`m_2` = First sample mass of water =
`100\ \text{g}`

`\Delta T_1` = Change in temperature of the first sample of water =
`T-60`

`T` = Final temperature of the mixture

`c` = Specific heat of water

Heat lost by water will be equal to the heat gained so we get

`m_1c\Delta T_1=m_2c\Delta T_2\\\Rightarrow 75(25-T)=100(T-60)\\\Rightarrow 0.75(25-T)=T-60\\\Rightarrow 18.75-0.75T=T-60\\\Rightarrow 18.75+60=T+0.75T\\\Rightarrow 78.75=1.75T\\\Rightarrow T=(78.75)/(1.75)\\\Rightarrow T=45\ ^(\circ)\text{C}`

The final temperature of the water is 45.