114.0 g of water is heated using 67.0 W of power with perfect efficiency. Ho long will it take to raise the temperature of the water from 15 C to 25 C?
320.000 s
To find the time it takes to raise the temperature of the water, we can use the formula:
Q = mcΔT
Where:
Q = heat energy (in joules)
m = mass of the water (in kg)
c = specific heat capacity of water (approximately 4.18 J/g°C or 4180 J/kg°C)
ΔT = change in temperature (in °C)
First, let's convert the mass of water from grams to kilograms:
mass (m) = 114.0 g = 0.114 kg
Next, let's calculate the heat energy required to raise the temperature of the water from 15°C to 25°C:
ΔT = 25°C - 15°C = 10°C
Now we can plug the values into the formula to find the heat energy (Q):
Q = (0.114 kg) × (4180 J/kg°C) × (10°C)
Q = 4789.2 J
Since the power (P) is given in Watts and it represents energy per unit time (J/s), we can write:
P = Q / t (where t is the time in seconds)
Now we can rearrange the formula to solve for time (t):
t = Q / P
Plugging in the values:
t = 4789.2 J / 67.0 W
t ≈ 71.4 seconds
Therefore, it will take approximately 71.4 seconds to raise the temperature of the water from 15°C to 25°C.
To calculate the time required to raise the temperature of water, we need to use the formula:
Q = m × c × ΔT
Where:
- Q is the heat energy transferred (in Joules)
- m is the mass of water (in kilograms)
- c is the specific heat capacity of water (approximately 4.18 J/g°C or 4180 J/kg°C)
- ΔT is the change in temperature (in Celsius)
First, let's convert the mass of water from grams to kilograms:
114.0 g = 0.114 kg
Next, we can calculate the heat energy transferred (Q) using the formula above:
Q = 0.114 kg × 4180 J/kg°C × (25 - 15)°C
Q = 0.114 kg × 4180 J/kg°C × 10°C
Q = 4789.2 J
Now, we need to determine the time (t) using the formula:
t = Q / P
Where:
- t is the time (in seconds)
- Q is the heat energy transferred (in Joules)
- P is the power (in Watts)
Plugging in the values:
t = 4789.2 J / 67.0 W
t ≈ 71.4 seconds
Therefore, it will take approximately 71.4 seconds to raise the temperature of the water from 15°C to 25°C.