If you pour equal amounts of scalding hot water into different metallic cups of equal temperature, which cup will heat up the most?
Rank the cups from hottest to coldest.
Rank from warmest to coolest final temperature.
500-g cast iron cup
500-g gold cup
750-g cast iron cup
q = mass x specific heat metal x delta T. Solve for delta T.
delta T = q/mass*sp.h.
So q is contant. mass is shown. sp.h. you can look up. Therefore, it appears to me that mass * sp.h. for each of th4ese and the smallest into a constant q will give the largest delta T.
To determine which cup will heat up the most and rank the cups from hottest to coldest, you need to consider the concept of specific heat capacity. Specific heat capacity is the amount of heat energy required to raise the temperature of a given mass of a substance by a certain amount. The formula for heat energy is Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the heat energy (Q) is the same for all the cups since equal amounts of hot water are poured into each cup. The mass (m) is different for each cup, and the specific heat capacity (c) varies for different metals.
Cast iron has a specific heat capacity of around 0.45 J/g°C, while gold has a specific heat capacity of around 0.13 J/g°C. It means that cast iron requires more heat energy to raise its temperature compared to gold.
Let's calculate the final temperature for each cup by assuming the initial temperature of the cups is the same:
For the 500-g cast iron cup:
Q = mcΔT
Q = (500 g)(0.45 J/g°C)(ΔT)
For the 500-g gold cup:
Q = mcΔT
Q = (500 g)(0.13 J/g°C)(ΔT)
For the 750-g cast iron cup:
Q = mcΔT
Q = (750 g)(0.45 J/g°C)(ΔT)
Since the heat energy (Q) is the same for each cup, we can set up the following equation:
(500 g)(0.45 J/g°C)(ΔT) = (500 g)(0.13 J/g°C)(ΔT) = (750 g)(0.45 J/g°C)(ΔT)
Since both the mass and specific heat capacity cancel out, the equation simplifies to:
ΔT = ΔT = ΔT
This means that all the cups will have the same final temperature when equal amounts of hot water of the same temperature are poured in. So, the ranking of the cups from hottest to coldest is not possible since they will reach the same final temperature.
Therefore, the cups' ranking from warmest to coolest final temperature is:
500-g cast iron cup, 500-g gold cup, 750-g cast iron cup (all with the same final temperature).
To determine which cup will heat up the most and rank them from hottest to coldest, we need to consider the specific heat capacity of each metal. The specific heat capacity is the amount of heat energy required to raise the temperature of a given amount of substance by 1 degree Celsius.
1. Determine the specific heat capacity of the metals:
- The specific heat capacity of cast iron is 0.46 J/g°C.
- The specific heat capacity of gold is 0.13 J/g°C.
2. Calculate the amount of heat energy needed to raise the temperature of each cup:
- For the 500-g cast iron cup: Q = (mass) x (specific heat capacity) x (change in temperature) = (500 g) x (0.46 J/g°C) x (T1 - T0)
- For the 500-g gold cup: Q = (mass) x (specific heat capacity) x (change in temperature) = (500 g) x (0.13 J/g°C) x (T1 - T0)
- For the 750-g cast iron cup: Q = (mass) x (specific heat capacity) x (change in temperature) = (750 g) x (0.46 J/g°C) x (T1 - T0)
3. Since we're pouring equal amounts of scalding hot water into the cups, we can assume the change in temperature is the same for all cups, T1 - T0.
4. However, the 500-g cast iron cup will heat up the most because it has both the highest mass and a relatively high specific heat capacity compared to gold.
Therefore, we can rank the cups from hottest to coldest:
1. 500-g cast iron cup
2. 750-g cast iron cup
3. 500-g gold cup
Note: The final temperature of each cup can't be determined without the specific temperature of the scalding hot water and taking into account heat losses to the surroundings. This ranking only considers the relative heating between the cups.