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two pots of water are on a stove. pot a contains 2 liters of water at room temperature and pot b contains 6 liters of water at room temperature. If you add heat to pot a for 5 minutes the temperature of the water increases by 2 degrees Celsius. If you add the same amount of heat to pot b how long will it take for the temperature of the water to increase by the same two degrees?

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Final answer:

To find the time it takes for the temperature of the water in pot B to increase by 2 degrees Celsius, you can use the concept of specific heat capacity. By using the equation Q = m * c * ΔT, where Q is the amount of heat energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature, you can calculate the amount of heat transferred and then use the equation t = Q / P, where t is the time, Q is the amount of heat energy, and P is the power, to find the time it takes.

Step-by-step explanation:

To find the time it takes for the temperature of the water in pot B to increase by 2 degrees Celsius, we can use the concept of specific heat capacity. Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius per unit mass. The specific heat capacity of water is approximately 4.18 J/g°C.

In this case, both pots have different amounts of water, so we need to consider the mass of water in each pot. Pot A contains 2 liters of water, which is equivalent to 2000 grams (since 1 liter of water is equal to 1000 grams). Pot B contains 6 liters of water, which is equivalent to 6000 grams.

Since the amount of heat added is the same for both pots (resulting in a 2-degree Celsius increase in temperature), we can use the equation:

Q = m * c * ΔT

where Q is the amount of heat energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.

For pot A, we have:

QA = 2000 g * 4.18 J/g°C * 2°C = 16,720 J

Now, we can rearrange the equation to solve for the time:

t = Q / P

where t is the time, Q is the amount of heat energy (16,720 J), and P is the power. Since the power is the rate at which heat is transferred, it is given as 500 W (watts).

For pot B, we have:

QB = 6000 g * 4.18 J/g°C * 2°C = 50,160 J

tB = QB / P = 50,160 J / 500 W = 100.32 seconds

Therefore, it would take approximately 100.32 seconds for the temperature of the water in pot B to increase by 2 degrees Celsius when the same amount of heat is added.

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