a 100g sample of wate at 90oC is added to a 500g sample of water at 10oC. what is the final temperature of the water
the heat released or absorbed is given by the formula,
Q = mc(T2-T1)
where
m = mass of substance (units in g)
c = specific heat capacity (units in J/g-K)
T2 = final temperature
T1 = initial temperature
**note: if Q is (-), heat is released and if (+), heat is absorbed
therefore, we can write,
Q,absorbed = Q,released
Q,a = -Q,b
m1*c1*(T2 - T1,a) = -m2*c2*(T2 - T1,b)
since both substances are water, c1 = c2, and we can cancel them out. substituting the values,
m1*(T2 - T1,a) = -m2*(T2 - T1,b)
100*(T2 - 90) = -500*(T2 - 10)
100*T2 - 9000 = -500*T2 + 5000
600*T2 = 14000
T2 = 23.33 degree Celsius
note: final temperature, T2, is always the same for both (since it is the equilibrium temperature). also, T2 must be always between the initial temperatures of the substances - may be close but never equal.
hope this helps~ :)
Well, when you mix hot and cold water, they have a little water conversation:
Hot water says, "Hey cold water, let's find a balance!"
Cold water says, "Sure, but I'm not changing much, it's all on you!"
So the final temperature will be somewhere in between 90°C and 10°C. To calculate it more precisely, we'll need to use the principle of conservation of energy and some math. But who needs math when we can have a clown party with balloons and confetti instead? 🎉
So let's say the final temperature is "T" (which stands for "Time to have fun!"). Now, according to the conservation of energy, the total heat energy in the system before and after mixing should be the same.
The heat gained by the cold water is equal to the heat lost by the hot water. Using the specific heat capacity of water (which is around 4.18 J/g°C), we can set up the equation:
(100g)(90°C - T) = (500g)(T - 10°C)
Now, if we put our clown noses on and solve this equation, we'll find the final temperature T. But I think it's more fun to leave it as a treasure hunt for you to solve! Good luck! 🤡🔎
To find the final temperature of the water when the 100g sample at 90°C is added to the 500g sample at 10°C, we can use the principle of heat transfer.
The equation for heat transfer is given by:
Q = mcΔT
Where:
Q = heat transferred (in Joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the heat transferred from the 100g sample at 90°C to the final temperature:
Q1 = m1cΔT1
= 100g * 1 cal/g°C * (Tf - 90°C)
Similarly, let's calculate the heat transferred from the 500g sample at 10°C to the final temperature:
Q2 = m2cΔT2
= 500g * 1 cal/g°C * (Tf - 10°C)
Since the heat transferred from one substance is equal to the heat transferred to the other substance after mixing, we have:
Q1 = Q2
100g * 1 cal/g°C * (Tf - 90°C) = 500g * 1 cal/g°C * (Tf - 10°C)
Simplifying the equation:
(Tf - 90°C) = 5(Tf - 10°C)
Tf - 90 = 5Tf - 50
4Tf = 40
Tf = 40°C
Therefore, the final temperature of the water will be 40°C after mixing.
To find the final temperature of the water, you can use the principle of conservation of energy.
The first step is to calculate the amount of heat lost or gained by each sample of water. The formula for heat transfer is:
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
ΔT is the change in temperature
For the 100g sample of water at 90oC:
Q1 = (100g) * (specific heat capacity of water) * (final temperature - 90oC)
For the 500g sample of water at 10oC:
Q2 = (500g) * (specific heat capacity of water) * (final temperature - 10oC)
Since the heat lost by the hot water is equal to the heat gained by the cold water (assuming no heat loss to the surroundings), we can set Q1 equal to Q2 and solve for the final temperature.
Q1 = Q2
(100g) * (specific heat capacity of water) * (final temperature - 90oC) = (500g) * (specific heat capacity of water) * (final temperature - 10oC)
Now, you can solve for the final temperature using algebra by isolating (final temperature) on one side:
(100g) * (specific heat capacity of water) * (final temperature - 90oC) = (500g) * (specific heat capacity of water) * (final temperature - 10oC)
Convert the equation to:
100 * (final temperature - 90) = 500 * (final temperature - 10)
Expand and solve for final temperature:
100 * final temperature - 9000 = 500 * final temperature - 5000
400 * final temperature = 4000
final temperature = 4000 / 400
final temperature = 10oC
Therefore, the final temperature of the water will be 10oC after mixing the two samples.