what will be the final temperature of a 514-g sample of water, intially at 10.0 celsius, after 90.8 kilo joules have been added o it ?
31.1
To find the final temperature of the water, we can use the equation:
q = mcΔT
Where:
q is the heat added to the water,
m is the mass of the water,
c is the specific heat capacity of water,
ΔT is the change in temperature.
First, let's calculate the heat added to the water:
q = 90.8 kJ = 90,800 J
Next, let's find the specific heat capacity of water:
c = 4.18 J/g°C (rounded to two decimal places)
Now, we can use the equation to find the change in temperature (ΔT):
90,800 J = 514 g × 4.18 J/g°C × ΔT
Simplifying the equation:
90,800 J = 2,149.72 g°C × ΔT
Dividing both sides by 2,149.72 g°C:
ΔT = 90,800 J / 2,149.72 g°C
ΔT ≈ 42.26 °C
Finally, we can calculate the final temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 10.0 °C + 42.26 °C
Final temperature ≈ 52.26 °C
Therefore, the final temperature of the water will be approximately 52.26 degrees Celsius.
To determine the final temperature of the water, we need to use the formula for heat transfer:
q = mcΔT
Where:
q is the heat transfer (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g·°C), and
ΔT is the change in temperature (in °C).
In this case, the mass of the water is given as 514 grams, the initial temperature is 10.0 °C, and the heat added is 90.8 kilojoules, which is equal to 90,800 joules (since 1 kilojoule = 1000 joules).
First, we need to convert the given heat from kilojoules to joules:
90.8 kilojoules = 90.8 × 1000 = 90,800 joules
Next, we rearrange the formula to solve for ΔT:
ΔT = q / (mc)
Now we can substitute the known values into the formula using the specific heat capacity of water, which is approximately 4.18 J/g·°C:
ΔT = 90,800 joules / (514 grams × 4.18 J/g·°C)
Calculating this equation will give us the change in temperature (ΔT). The final temperature can be found by adding the change in temperature (ΔT) to the initial temperature:
final temperature = initial temperature + ΔT
Using the given values, the calculation would be as follows:
ΔT = 90,800 J / (514 g × 4.18 J/g·°C)
ΔT ≈ 43.7 °C
Therefore, the final temperature of the water would be:
final temperature = 10.0 °C + 43.7 °C
final temperature ≈ 53.7 °C
So, the final temperature of the water would be approximately 53.7 °C.