Question

50 g of water at 20ºC is mixed with 50 g of water at 40ºC. The temperature of the mixture in equilibrium is.

• A. 30ºC
• B. 40ºC
• C. 50ºC
• D. 75ºC

Answer 1

The correct option is A

30ºC

The formula used to calculate the temperature of the mixture in equilibrium is:

If M₁ mass of liquid at ${\mathrm{T}}_1^{°}\mathrm{C}$ is mixed with M₂ mass of liquid at ${\mathrm{T}}_2^{°}\mathrm{C}$.

Then the temperature of the mixture in equilibrium is$\frac{({\mathrm{M}}_1\times {\mathrm{T}}_1)+({\mathrm{M}}_2\times {\mathrm{T}}_2)}{({\mathrm{M}}_1+{\mathrm{M}}_2)}$.

$50\mathrm{g}\left({\mathrm{M}}_1\right)$of water is mixed with $50\mathrm{g}\left({\mathrm{M}}_2\right)$ of water at ${40}^{°}\mathrm{C}\left({\mathrm{T}}_2^{°}\mathrm{C}\right)$. The temperature of the mixture in equilibrium is$\frac{(50\times 20)+(50\times 40)}{(50+50)}=\frac{50\times (20+40)}{\left(100\right)}=\frac{20+40}{2}=\frac{60}{2}=30°\mathrm{C}$.

Conclusion statement: 50 g of water at 20ºC is mixed with 50 g of water at 40ºC. The temperature of the mixture in equilibrium is 30ºC.