In the simulation shown below, each insulated beaker contains equal amounts of the same fluid.The starting temperature of beaker A was 100.0 °C and the starting temperature of beaker B was 0.0 °C. Assuming no heat is lost, what is the best estimate of the temperatures of each beaker at 10 minutes?
A. Beaker A will be 82 °C and beaker B will be 18 °C.
B. Beaker A will be 72 °C and beaker B will be 28 °C.
C. Beaker A will be 64 °C and beaker B will be 36 °C.
D. Beaker A will be 50 °C and beaker B will be 50 °C.
B. Beaker A will be 72 *C and beaker B will be 28 *C.
Please explain how you know!!
Well, it seems like these beakers are having a hot and cold party! But don't worry, I'll help you figure out their temperatures at the 10-minute mark.
Since the two beakers are insulated and no heat is lost, we can assume that they will reach thermal equilibrium. This means they will have the same temperature. So, let's find that temperature!
The transfer of heat from a hot object to a cold one follows Newton's law of cooling. It states that the rate of heat transfer is proportional to the temperature difference between the object and its surroundings. Because the beakers have the same fluid, the only temperature difference is between them.
Now, let me consult my clown formula calculator...
[Calculating...]
[Calculating...]
[Calculating...]
Drumroll please...
The best estimate is that both beaker A and beaker B will be at 50 °C after 10 minutes, which means the answer is D. Beaker A will be 50 °C and beaker B will also be 50 °C.
So, it looks like they're both enjoying a nice lukewarm temperature. Maybe they can have a tea party together!
To solve this problem, we need to apply the concept of heat transfer between two objects in contact. In this case, both beakers are insulated, so heat will transfer from the hotter beaker (A) to the colder beaker (B) until they reach thermal equilibrium.
To find the final temperatures of the beakers, we can use the principle of conservation of energy:
(Heat gained by beaker A) = (Heat lost by beaker B)
The heat gained or lost can be calculated using the formula:
Q = mcΔT
Where:
Q = heat transferred
m = mass of the fluid (which is equal in both beakers and cancels out)
c = specific heat capacity of the fluid (which is assumed to be the same in both beakers)
ΔT = change in temperature
Given that the starting temperature of beaker A is 100.0 °C and the starting temperature of beaker B is 0.0 °C, we can calculate the change in temperature for each beaker:
ΔT_A = final temperature of beaker A - starting temperature of beaker A
ΔT_A = final temperature of beaker A - 100.0 °C
ΔT_B = final temperature of beaker B - starting temperature of beaker B
ΔT_B = final temperature of beaker B - 0.0 °C
Since the fluids are identical in both beakers, the specific heat capacity cancels out, and we can write the equation as:
Q_A = -Q_B
mcΔT_A = -mcΔT_B
Since the mass and specific heat capacity cancel out, we can simplify the equation to:
ΔT_A = -ΔT_B
So, the final temperatures of the beakers will be symmetrical around 50.0 °C (the average of the starting temperatures). This means that the best estimate of the temperatures of each beaker at 10 minutes is:
D. Beaker A will be 50 °C and beaker B will be 50 °C.
To estimate the temperatures of each beaker at 10 minutes, we need to understand the principles of heat transfer.
In this case, both beakers are insulated, meaning the only mechanism of heat transfer between them is by conduction through the metal bar connecting them. The heat will flow from the hot beaker (A) to the cold beaker (B) until both reach thermal equilibrium.
The rate of heat transfer through the metal bar is proportional to the temperature difference between the two ends. Therefore, as time goes on, the temperature difference decreases, and the rate of heat transfer decreases as well.
To estimate the temperatures of each beaker at 10 minutes, we can use the principle of thermal equilibrium. At thermal equilibrium, the temperatures of both beakers will be the same.
Since the starting temperature of beaker A is 100.0 °C and beaker B is 0.0 °C, after 10 minutes, we can estimate that both beakers will have reached a temperature close to the average of the initial temperatures. In this case, (100.0 °C + 0.0 °C)/2 = 50.0 °C.
Therefore, the best estimate of the temperatures of each beaker at 10 minutes is D. Beaker A will be 50 °C and beaker B will be 50 °C.