To what temperature will 7700 J of heat raise 3.0 kg of water that is initially at 10.0 degrees C?
To calculate the temperature to which 7700 J of heat will raise 3.0 kg of water, we can use the specific heat capacity equation:
Q = mcΔT,
where:
Q is the amount of heat transferred,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
In this case, the mass of water (m) is 3.0 kg, the specific heat capacity of water (c) is 4.184 J/g°C (or 4184 J/kg°C), and the initial temperature (T₁) is 10.0°C.
Converting the mass from kg to grams:
m = 3.0 kg = 3000 g
Now we rearrange the equation to solve for ΔT:
Q = mcΔT
ΔT = Q / mc
Plugging in the given values:
ΔT = 7700 J / (3000 g × 4.184 J/g°C)
Calculating:
ΔT ≈ 0.616 °C
So, the temperature will be raised by approximately 0.616 degrees Celsius. To find the final temperature, we add this change to the initial temperature:
T₂ = T₁ + ΔT
T₂ = 10.0 °C + 0.616 °C
Calculating:
T₂ ≈ 10.616 °C
Therefore, the temperature will be raised to approximately 10.616 degrees Celsius.
To determine the final temperature to which the water will be raised, we can use the equation:
\(Q = m \cdot c \cdot \Delta T\)
Where:
- Q is the heat energy (in Joules).
- m is the mass of the water (in kg).
- c is the specific heat capacity of water (which is 4186 J/kg·°C).
- ΔT is the change in temperature (in °C).
We have the values:
- Q = 7700 J
- m = 3.0 kg
- c = 4186 J/kg·°C
- Initial temperature (T1) = 10.0 °C
First, let's rearrange the equation to solve for ΔT:
\(\Delta T = \frac{Q}{m \cdot c}\)
Substituting the given values, we have:
\(\Delta T = \frac{7700 \, \text{J}}{3.0 \, \text{kg} \cdot 4186 \, \text{J/kg·°C}}\)
Now we can calculate ΔT:
\(\Delta T = 0.615 \, \text{°C}\)
To find the final temperature (T2), we add ΔT to the initial temperature:
\(T2 = T1 + \Delta T\)
Substituting the values:
\(T2 = 10.0 °C + 0.615 °C\)
Calculating:
\(T2 \approx 10.615 °C\)
Therefore, the final temperature to which the water will be raised is approximately 10.615 °C.