8. What would be the final temperature of the mixture when .5 g of ice at -10 degree are mixed with 250g of water at 30 degree centigrade? S.H.C of ice 0.5cal/g degree centigrade and S.L.H of ice = 80cal/g.
To find the final temperature of the mixture, we can use the principle of conservation of energy. The energy gained by the water will be equal to the energy lost by the ice.
First, let's find the energy lost by the ice.
Energy lost by ice = mass of ice (in grams) * specific heat capacity of ice (0.5 cal/g °C) * change in temperature (final temperature - initial temperature)
Mass of ice = 0.5 g
Specific heat capacity of ice = 0.5 cal/g °C
Initial temperature of ice = -10 °C
Since we are given the initial temperature of the ice, we need to solve for the final temperature of the ice before we can calculate the energy lost. We can do this using the heat gained by the water.
Heat gained by water = mass of water (in grams) * specific heat capacity of water * change in temperature (final temperature of the mixture - initial temperature of water)
Mass of water = 250 g
Specific heat capacity of water = 1 cal/g °C
Initial temperature of water = 30 °C
The heat gained by the water will be equal to the energy lost by the ice.
Heat gained by water = Energy lost by ice
Substituting the values we have:
250 g * 1 cal/g °C * (final temperature of the mixture - 30 °C) = 0.5 g * 0.5 cal/g °C * (final temperature of the mixture - (-10 °C))
Now, we can solve this equation to find the final temperature of the mixture by isolating the variable:
250 * (final temperature of the mixture - 30) = 0.5 * 0.5 * (final temperature of the mixture + 10)
Simplifying the equation:
250 * final temperature of the mixture - 7500 = 0.25 * final temperature of the mixture + 2.5
249.75 * final temperature of the mixture - 7500 = 0.25 * final temperature of the mixture
249.75 * final temperature of the mixture - 0.25 * final temperature of the mixture = 7500
249.5 * final temperature of the mixture = 7500
final temperature of the mixture = 7500 / 249.5
final temperature of the mixture ≈ 30.12 °C
Therefore, the final temperature of the mixture would be approximately 30.12 °C.
To find the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the water is equal to the heat gained by the ice.
First, let's calculate the heat lost by the water. We can use the formula:
Q = m * c * ΔT
Where:
Q = heat lost by water
m = mass of water
c = specific heat capacity of water
ΔT = change in temperature
Given:
m = 250g
c = 1 cal/g°C (Specific heat capacity of water)
ΔT = final temperature - initial temperature
Since the initial temperature of the water is 30°C, we can rewrite the formula as:
Q = m * c * (final temperature - 30°C)
Now, let's calculate the heat gained by the ice. We can use the formula:
Q = m * L
Where:
Q = heat gained by ice
m = mass of ice
L = Latent heat of fusion
Given:
m = 0.5g
L = 80 cal/g (Latent heat of fusion of ice)
Now, equating both equations:
m * c * (final temperature - 30°C) = m * L
Substituting the given values:
250g * 1 cal/g°C * (final temperature - 30°C) = 0.5g * 80 cal/g
Simplifying the equation:
(250g * (final temperature - 30°C)) = 40g
Dividing both sides by 250g:
final temperature - 30°C = 0.16°C
Adding 30°C to both sides:
final temperature = 30.16°C
Therefore, the final temperature of the mixture is 30.16°C.