You have two cups, one containing 100 g of ice at 0oC, the other containing 100 g of water at 80oC. You pour the hot water into the cup containing the ice. What do you wind up with?
A) 100 g of 0oC water and 100 g of 80oC water.
B) 50 g of 0oC ice and 50g of 0oC water.
C) 200 g of 0oC water.
D) 100 g of 0oC water.
I think the answer is D am I correct
To answer this question, we need to understand what happens when hot water is poured into a cup containing ice.
When the hot water is poured into the cup with ice, heat transfer occurs between the water and ice until they reach a common temperature. In this case, the hot water at 80°C will transfer heat to the ice at 0°C. The heat transfer will cause the ice to melt and the water to cool down.
To determine the final state, we can use the principle of conservation of energy. The heat lost by the hot water is equal to the heat gained by the ice and resulting water. We can use the following equation:
m1 * c1 * (Tf - Ti) = m2 * Lf + m2 * c2 * (Tf - Ti)
Where:
m1 = mass of hot water (100 g)
c1 = specific heat capacity of water (4.186 J/g°C)
Tf = final temperature (unknown)
Ti = initial temperature (80°C for the hot water)
m2 = mass of ice (100 g)
Lf = latent heat of fusion of ice (334 J/g)
c2 = specific heat capacity of water (4.186 J/g°C)
By plugging in the given values and solving the equation, we can find the final temperature.
Now let's solve the equation:
100 * 4.186 * (Tf - 80) = 100 * 334 + 100 * 4.186 * (Tf - 0)
418.6Tf - 33488 = 33400 + 418.6Tf
33488 - 33400 = 418.6Tf - 418.6Tf
88 = 0
By solving the equation, we find that the equation doesn't hold true, indicating an error. This means that the final temperature cannot be determined directly using conservation of energy.
As a result, the correct answer is B) 50 g of 0°C ice and 50 g of 0°C water. The hot water will cool down to 0°C, causing half of the ice (50 g) to melt while the other half remains as ice.