What will be the final temperature if 1600 cal of heat is given to an ice block of mass 20 grams?
0 degree celcius
To find the final temperature when heat is given to an ice block, we can use the equation:
Q = mcΔT
where:
Q is the heat energy
m is the mass of the ice block
c is the specific heat capacity of water
ΔT is the change in temperature
Given:
Q = 1600 cal
m = 20 grams
First, let's convert the mass from grams to kilograms:
m = 20 grams ÷ 1000 = 0.02 kg
Next, we need to determine the specific heat capacity of water. The specific heat capacity of water is 1 calorie/gram°C.
Now we can rearrange the equation to solve for ΔT:
ΔT = Q / (mc)
ΔT = 1600 cal / (0.02 kg * 1 cal/gram°C)
Simplifying, we have:
ΔT = 1600 cal / (0.02 kg * 1 cal/g°C)
ΔT = 1600 cal / (0.02 kg°C)
Finally, calculating the value:
ΔT = 80000 °C/kg
Therefore, the change in temperature is 80000 °C per kilogram.
Since negative temperature values are not considered in this context, we can assume that the ice block will reach 0 °C. So the final temperature will be 0 °C.
To find the final temperature of the ice block, we need to use the specific heat formula. The formula is:
Q = m * c * ΔT
Where:
Q is the heat energy absorbed or released
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
First, let's convert the mass of the ice block from grams to kilograms to match the unit of the specific heat capacity.
Mass = 20 grams = 20 / 1000 = 0.02 kg
The specific heat capacity of ice is approximately 2.09 J/g°C.
Now, we can rearrange the formula to solve for ΔT:
ΔT = Q / (m * c)
Plugging in the values:
ΔT = 1600 cal / (0.02 kg * 2.09 J/g°C)
Now, let's convert calories to joules by using the conversion factor:
1 cal = 4.18 J
ΔT = 1600 cal * 4.18 J/cal / (0.02 kg * 2.09 J/g°C)
Simplifying:
ΔT = 6688 J / (0.0418 kg * 2.09 J/g°C)
ΔT = 6688 J / 0.087162 kg°C
Finally, calculating ΔT:
ΔT ≈ 76.701 °C
To find the final temperature, we need to know the initial temperature of the ice block. If the initial temperature is 0°C (assuming it's ice at its freezing point), then the final temperature would be:
Final temperature = Initial temperature + ΔT
Final temperature = 0°C + 76.701 °C
Final temperature ≈ 76.701 °C
So, if 1600 cal of heat is given to an ice block of mass 20 grams at 0°C, the final temperature will be approximately 76.701 °C.