Chapter U5, Problem C18.7RE

Interpretation Introduction

Interpretation:

Final temperature must be calculated when 70 g of hot water at 85°C is mixed with 50 g of cold water at 18°C.

Concept Introduction:

As per Calorimetry principle, when a hot object is kept in contact with cold object then the hot object will release heat which will be absorbed by the cold object. The process continues until the temperature of both the object is same. This means thermal equilibrium is attained.

  $\text{t=}\frac{{\text{m}}_{\text{1}}{\text{t}}_{\text{1}}{\text{+m}}_{\text{2}}{\text{t}}_{\text{2}}}{{\text{m}}_{\text{1}}{\text{+m}}_{\text{2}}}$ where m₁ and m₂ are masses of two water samples and t₁ and t₂ are temperatures of the two water samples respectively.

Answer to Problem C18.7RE

Final temperature of the mixture of water is 57.08°C.

Explanation of Solution

The final temperature can be calculated as follows:

  $\text{t=}\frac{{\text{m}}_{\text{1}}{\text{t}}_{\text{1}}{\text{+m}}_{\text{2}}{\text{t}}_{\text{2}}}{{\text{m}}_{\text{1}}{\text{+m}}_{\text{2}}}\text{=}\frac{\text{70×85+50×18}}{\text{70+50}}\text{ °C =}\frac{\text{5950}}{\text{120}}\text{ °C= 57}\text{.08°C}\text{.}$

Putting all the vales final temperature of the mixture of water is found.

Conclusion

Final temperature was found to be 57.08°C.