1.In a device like the one shown below, the cylinder is allowed to fall a distance of 300 m. As a result, the temperature of the water increases by 2.7°C. What would have been the increase in temperature if the cylinder were only allowed to fall 100 m
Without seeing the device, I would assume you could apply the equation shown below.
300/2.7 = 100/x or
2.7/300 = x/100
Solve for x.
0.9
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In a device like the one shown below, the cylinder is allowed to fall a distance of 300 m. As a result, the temperature of the water increases by 2.7°C. What would have been the increase in temperature if the cylinder were only allowed to fall 100 m?
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To determine the increase in temperature if the cylinder were only allowed to fall 100 m, we need to understand the relationship between the distance the cylinder falls and the resulting increase in temperature.
One way to approach this problem is to use the concept of potential energy and heat capacity. The potential energy gained by the falling cylinder is converted into thermal energy, resulting in an increase in temperature.
The potential energy gained by an object falling from a height is given by the formula:
Potential Energy = mass * gravitational acceleration * height
In this case, the height is 300 m when the cylinder falls. Let's assume the mass of the falling object is 1 kg and the gravitational acceleration is approximately 9.8 m/s².
Potential Energy = 1 kg * 9.8 m/s² * 300 m
Potential Energy = 2940 J
Now, let's consider the heat capacity. Heat capacity is a measure of the amount of thermal energy required to raise the temperature of a substance by a certain amount. For water, the specific heat capacity is approximately 4.18 J/g°C.
To find the increase in temperature, we need to divide the potential energy gained by the heat capacity, while taking into account the mass of the water.
Water has a density of approximately 1 g/mL, so if the cylinder falls by 300 m, it displaces a volume of 300 mL (which is equivalent to 300 g) of water.
Increase in Temperature = Potential Energy / (mass of water * heat capacity)
Increase in Temperature = 2940 J / (300 g * 4.18 J/g°C)
Increase in Temperature ≈ 2.63 °C
Therefore, if the cylinder were only allowed to fall 100 m, you can follow the same steps using the new height to find the increase in temperature.
Potential Energy = 1 kg * 9.8 m/s² * 100 m
Potential Energy = 980 J
Increase in Temperature = Potential Energy / (mass of water * heat capacity)
Using the same values for the mass of water and heat capacity as before,
Increase in Temperature = 980 J / (300 g * 4.18 J/g°C)
Increase in Temperature ≈ 0.98 °C
So, if the cylinder were only allowed to fall 100 m, the increase in temperature would be approximately 0.98 °C.