300 gm of water at 25°c is added to 100 gm of ice at 0°c.the temperature of the mixture is?
The answer is wrong zero is the answer
To find the final temperature of the mixture, we can use the principle of conservation of energy.
First, let's calculate the heat gained by the water and the heat lost by the ice:
Heat gained by water = mass * specific heat capacity * change in temperature
Heat gained by water = 300g * 4.18 J/g°C * (final temperature - 25°C)
Heat lost by ice = mass * specific heat capacity * change in temperature
Heat lost by ice = 100g * 2.09 J/g°C * (0°C - final temperature)
According to the principle of conservation of energy, the heat gained by the water equals the heat lost by the ice:
300g * 4.18 J/g°C * (final temperature - 25°C) = 100g * 2.09 J/g°C * (0°C - final temperature)
Now, let's solve for the final temperature:
300g * 4.18 J/g°C * final temperature - 300g * 4.18 J/g°C * 25°C = 100g * 2.09 J/g°C * 0°C - 100g * 2.09 J/g°C * final temperature
1254g * final temperature - 31350 J = 0 J - 208g * final temperature
1462g * final temperature = 31350 J
final temperature = 31350 J / 1462g
final temperature ≈ 21.47°C
Therefore, the temperature of the mixture is approximately 21.47°C.
To find the final temperature of the mixture, we can use the principle of conservation of energy.
Step 1: Determine the energy exchanged during the process.
The energy exchanged, Q, can be calculated using the formula:
Q = m₁ * c₁ * ΔT₁ + m₂ * c₂ * ΔT₂
where:
m₁ = mass of water
c₁ = specific heat capacity of water
ΔT₁ = change in temperature of water
m₂ = mass of ice
c₂ = specific heat capacity of ice
ΔT₂ = change in temperature of ice
In this case, the ice is at its melting point (0°C), so the change in temperature of ice (ΔT₂) is zero.
Step 2: Determine the specific heat capacity values for water and ice.
The specific heat capacity of water is approximately 4.18 J/g°C.
The specific heat capacity of ice is approximately 2.09 J/g°C.
Step 3: Calculate the energy exchanged.
Q = (300 g * 4.18 J/g°C * (T - 25°C)) + (100 g * 2.09 J/g°C * (0°C - T))
We want to find the final temperature, T, of the mixture when the energy exchanged, Q, is zero.
Step 4: Solve for the final temperature (T).
Setting Q = 0, we can solve for T:
(300 g * 4.18 J/g°C * (T - 25°C)) + (100 g * 2.09 J/g°C * (0°C - T)) = 0
(1254 g * (T - 25°C)) + (-209 g * T) = 0
1254 g * T - 31350 g°C + (-209 g * T) = 0
1045 g * T = 31350 g°C
T = 31350 g°C / 1045 g
T = 30°C
Therefore, the final temperature of the mixture is 30°C.
Since the subject is 'maths', I'm assuming the energy required for the ice-to-water conversion is not to be considered
Basically, you have to multiply the fraction of the total masses of the substance with their temperature:
Final Temp. = (300/400)*25 + (100/400)*0
= (3/4)*25
= 18.75 degrees Celsius