If 8.00 kJ of heat are added to 200. g of water
at 20.0 �C, what is the final temperature of
the water?
Well, it looks like we have a hot situation here! Let me calculate the final temperature for you. Just give me a moment to crunch the numbers. *Beep boop beep.* Ah, got it! The final temperature of the water is... drumroll, please... 67.5 degrees Celsius! So, it seems the water got a little steamy after that heat was added. Stay cool!
To find the final temperature of water after adding heat, we can use the equation:
q = m * c * ΔT
Where:
q = heat added or lost
m = mass of the water (in grams)
c = specific heat capacity of water (4.18 J/g·°C)
ΔT = change in temperature
First, let's convert the heat added from kJ to J:
8.00 kJ = 8.00 * 1000 J = 8000 J
Now, let's calculate the change in temperature of the water:
q = m * c * ΔT
Rearranging the equation to solve for ΔT:
ΔT = q / (m * c)
ΔT = 8000 J / (200 g * 4.18 J/g·°C)
ΔT ≈ 19.14 °C
The change in temperature is approximately 19.14 °C.
To find the final temperature, we add the change in temperature to the initial temperature (20.0 °C):
Final temperature = Initial temperature + ΔT
Final temperature = 20.0 °C + 19.14 °C
Final temperature ≈ 39.14 °C
Therefore, the final temperature of the water is approximately 39.14 °C.
To find the final temperature of the water after adding heat, we need to use the formula for specific heat capacity.
The formula is:
q = mcΔT
where:
q represents the heat energy absorbed (in joules),
m represents the mass of the substance (in grams),
c represents the specific heat capacity of the substance (in J/g·°C),
ΔT represents the change in temperature (in °C).
Here, we are given:
q = 8.00 kJ = 8.00 × 10^3 J (since 1 kJ = 10^3 J)
m = 200. g
c = specific heat capacity of water = 4.18 J/g·°C (approximately)
ΔT = final temperature - initial temperature = unknown - 20.0 °C (since the initial temperature is given as 20.0 °C)
Rewriting the formula with the known values, we get:
8.00 × 10^3 J = (200. g) × (4.18 J/g·°C) × (unknown - 20.0 °C)
Simplifying further:
8.00 × 10^3 J = (836 g·°C) × (unknown - 20.0 °C)
Now we can solve for the unknown final temperature, 'unknown':
8.00 × 10^3 J = 836 g·°C × unknown - 836 g·°C × 20.0 °C
8.00 × 10^3 J = 836 g·°C × unknown - 16720 g·°C
Adding 16720 g·°C to both sides:
8.00 × 10^3 J + 16720 g·°C = 836 g·°C × unknown
Dividing both sides by 836 g·°C:
(8.00 × 10^3 J + 16720 g·°C) ÷ 836 g·°C = unknown
Calculating the expression on the left side, we find that:
(8.00 × 10^3 J + 16720 g·°C) ÷ 836 g·°C ≈ 40.1911
Therefore, the final temperature of the water is approximately 40.2 °C.
8,000 = mass x specific heat x (Tfinal-Tinitial)= ??
Solve for Tfinal.