Steam of 100 degree celsius is passed into ice of 100g . The mixture weighs 120g at 35 degree celsius, find the specific heat of ice.
What is the initial temperature of the ice?
0 degree celsius
You can't get specific heat of ice from this if it started at zero degree, it melted, and was never heated as ice.
To find the specific heat of ice, we can use the principle of energy conservation. The energy gained by the ice can be calculated by considering the heat absorbed from the steam and the heat lost during the cooling process.
First, let's calculate the heat absorbed by the ice from the steam. We can use the formula:
Q1 = m1 * Lf
where Q1 is the heat absorbed by the ice, m1 is the mass of the ice, and Lf is the latent heat of fusion for ice.
Given that the mass of ice (m1) is 100g and the latent heat of fusion for ice (Lf) is approximately 334 J/g, we can substitute these values into the equation:
Q1 = 100g * 334 J/g
Q1 = 33400 J
Next, let's calculate the heat lost during the cooling process. We can use the formula:
Q2 = m2 * c2 * ΔT
where Q2 is the heat lost, m2 is the mass of the mixture, c2 is the specific heat capacity of the mixture, and ΔT is the change in temperature.
Given that the mass of the mixture (m2) is 120g and the change in temperature (ΔT) is 100°C - 35°C = 65°C, we can substitute these values into the equation:
Q2 = 120g * c2 * 65°C
Now, since energy is conserved, the heat absorbed by the ice (Q1) is equal to the heat lost during the cooling process (Q2). Therefore,
Q1 = Q2
33400 J = 120g * c2 * 65°C
Now we can solve for the specific heat capacity of the mixture (c2):
c2 = 33400 J / (120g * 65°C)
c2 ≈ 4.27 J/(g·°C)
So, the specific heat capacity of ice is approximately 4.27 J/(g·°C).