What will be the final temperature if 1600 cal of heat is given to an ice block of mass 20 grams?
To find the final temperature, we need to use the specific heat formula and the concept of latent heat.
1. First, we need to calculate the energy required to heat the ice block from its initial temperature (0°C) to its melting point (0°C). The specific heat capacity of ice is 0.5 cal/g°C.
Energy = mass * specific heat * temperature change
Energy = 20 g * 0.5 cal/g°C * (0°C - 0°C)
Energy = 0 calories
Therefore, no energy is required to heat the ice block to its melting point.
2. Next, we need to calculate the energy required to melt the ice at its melting point (0°C). The latent heat of fusion for ice is 80 cal/g.
Energy = mass * latent heat
Energy = 20 g * 80 cal/g
Energy = 1600 calories
So, the 1600 calories of heat is now used to melt the ice completely.
3. After the ice melts, the temperature will start increasing. To find the change in temperature when all the ice is melted, we use the specific heat capacity of water, which is 1 cal/g°C.
Energy = mass * specific heat * temperature change
1600 cal = 20 g * 1 cal/g°C * temperature change
Solving for temperature change:
temperature change = 1600 cal / (20 g * 1 cal/g°C)
temperature change = 80°C
Therefore, the final temperature will increase by 80°C.
4. To find the final temperature, we need to add the initial temperature (0°C) to the temperature change.
Final temperature = initial temperature + temperature change
Final temperature = 0°C + 80°C
Final temperature = 80°C
Thus, the final temperature will be 80°C.
To find the final temperature, we can use the equation:
Q = m * c * ΔT
Where:
Q is the heat energy transferred,
m is the mass of the object,
c is the specific heat capacity of the object,
ΔT is the change in temperature.
In this case, we are given:
Q = 1600 cal,
m = 20 grams.
First, let's convert the mass into kilograms:
20 grams = 0.02 kg
Now, let's assume the ice block starts at 0°C. Since we want to find the final temperature, let's represent it as T_f.
The specific heat capacity of ice, c, is 0.5 cal/g°C.
Now, we can rearrange the equation to solve for the change in temperature:
ΔT = Q / (m * c)
Plugging in the values:
ΔT = 1600 cal / (0.02 kg * 0.5 cal/g°C)
ΔT = 1600 cal / (0.01 cal/°C)
ΔT = 160,000°C
Finally, to find the final temperature, we add the change in temperature to the initial temperature:
T_f = 0°C + 160,000°C
Therefore, the final temperature will be 160,000°C.