Consider Joule's experiment described in the insight below. Assume the mass m = 2.3 kg and the fluid is water with a volume of 1.75 L. What is the increase in the temperature of the water when the mass moves vertically a distance z = 1.55 m?
To calculate the increase in temperature of the water in Joule's experiment, we need to use the formula:
Q = m * c * ΔT
Where:
Q = heat transferred (in joules)
m = mass of the water (in kg)
c = specific heat capacity of water (in J/kg·°C)
ΔT = change in temperature (in °C)
Given:
m = 2.3 kg (mass of water)
V = 1.75 L (volume of water)
z = 1.55 m (vertical distance traveled by the mass)
To find the heat transferred (Q), we can use the formula:
Q = m * g * z
Where:
g = acceleration due to gravity (approximated as 9.8 m/s²)
We can calculate Q as follows:
Q = (2.3 kg) * (9.8 m/s²) * (1.55 m)
Now we need to convert the heat transferred into ΔT:
ΔT = Q / (m * c)
However, to use this formula, we need the specific heat capacity of water (c).
The specific heat capacity of water is approximately 4186 J/kg·°C.
Let's calculate the increase in temperature ΔT:
Q = (2.3 kg) * (9.8 m/s²) * (1.55 m)
Q = 34.057 J
ΔT = (34.057 J) / (2.3 kg * 4186 J/kg·°C)
Now we can calculate ΔT by dividing Q by (m * c):
ΔT = 34.057 J / (2.3 kg * 4186 J/kg·°C)
To determine the increase in temperature, we can use Joule's experiment, where the work done by a weight on a mass raises the temperature of a fluid.
The formula to calculate the increase in temperature (ΔT) using Joule's experiment is:
ΔT = (W / (m * Cp))
Where:
ΔT is the increase in temperature
W is the work done on the system
m is the mass of the fluid
Cp is the specific heat capacity of the fluid
In this case, we know the mass of the fluid (m = 2.3 kg) and the volume of the fluid (1.75 L). However, we need the specific heat capacity (Cp) of water to proceed.
The specific heat capacity of water is approximately 4.18 J/g·°C. To convert the volume of water to mass, we need to multiply the volume by its density, which is approximately 1 kg/L.
Mass of water = volume * density
= 1.75 L * 1 kg/L
= 1.75 kg
Now we have all the required values to calculate the increase in temperature.
First, we need to calculate the work done (W) using the formula:
W = m * g * z
Where:
W is the work done
m is the mass
g is the acceleration due to gravity (approximately 9.8 m/s^2)
z is the distance the mass moves vertically
Plugging in the given values:
W = 2.3 kg * 9.8 m/s^2 * 1.55 m
Calculating this, we get:
W ≈ 35.798 J
Now, we can calculate the increase in temperature:
ΔT = (W / (m * Cp))
= (35.798 J / (1.75 kg * 4.18 J/g·°C))
Calculating this, we get:
ΔT ≈ 4.14 °C
Therefore, the increase in temperature of the water is approximately 4.14 °C when the mass moves vertically a distance of 1.55 m.