While studying for this quiz you realize that you still have 100 g of lukewarm coffee at 40°C left in a paper cup. When you pour 50 g of boiling water into the cup, the temperature of the resulting coffee-like mixture will be now (please show me how to solve)
To determine the final temperature of the coffee-like mixture after pouring boiling water into the cup, you can use the principle of conservation of energy. The heat lost by the boiling water is equal to the heat gained by the lukewarm coffee.
First, we need to find out the initial heat content of the lukewarm coffee.
The specific heat capacity of water is approximately 4.18 J/g°C (joules per gram per degree Celsius), which means it takes 4.18 J of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
The initial temperature of the lukewarm coffee is 40°C, and it has a mass of 100 g. So the initial heat content of the coffee is:
Initial Heat Content = mass * specific heat capacity * temperature
= 100 g * 4.18 J/g°C * 40°C
= 16720 J
Next, we need to find out the heat gained by the lukewarm coffee when the boiling water is added.
The boiling water has a mass of 50 g and its initial temperature is 100°C (boiling point). To find the heat gained, we use the same formula:
Heat Gained = mass * specific heat capacity * change in temperature
Since the boiling water is added at 100°C, the change in temperature is the final temperature minus the initial temperature. Let's assume the final temperature is T°C:
Heat Gained = 50 g * 4.18 J/g°C * (T - 100°C)
= 209 J * (T - 100)
According to the principle of conservation of energy, the heat gained by the lukewarm coffee is equal to the heat lost by the boiling water:
Heat Gained = Heat Lost
209 J * (T - 100) = 16720 J
Now, we can solve for T by dividing both sides of the equation by 209 J and then adding 100 to both sides:
(T - 100) = 16720 J / 209 J
(T - 100) ≈ 80°C
T ≈ 80°C + 100
T ≈ 180°C
Therefore, the temperature of the resulting coffee-like mixture after pouring boiling water into the cup would be approximately 180°C.