1. Calculate the number of calories needed to increase the temperature of 50.0 g of copper metal from 21.0 degrees C to 75.0 degrees C. Given, the specific heat of copper is 0.382 cal/g x degrees C.
2. What will be the final temperature if 2000g of copper at 95 degrees C loses 10kcal of heat
1. To calculate the number of calories needed to increase the temperature of copper, we can use the formula:
Q = m x c x ΔT
Where:
Q = Heat energy (in calories)
m = Mass of the substance (in grams)
c = Specific heat capacity (in cal/g x degrees C)
ΔT = Change in temperature (in degrees C)
Given:
m = 50.0 g
c = 0.382 cal/g x degrees C
ΔT = (75.0 - 21.0) degrees C = 54.0 degrees C
Using the formula, we can calculate:
Q = (50.0 g) x (0.382 cal/g x degrees C) x (54.0 degrees C)
Q ≈ 912.84 calories
Therefore, approximately 912.84 calories are needed to increase the temperature of 50.0 g of copper from 21.0 degrees C to 75.0 degrees C.
2. To find the final temperature after losing heat, we can use the formula:
Q = m x c x ΔT
Rearranging the formula, we get:
ΔT = Q / (m x c)
Given:
Q = -10 kcal (negative sign indicates heat loss)
m = 2000 g
c = 0.382 cal/g x degrees C
Converting the units:
Q = -10 kcal = -10,000 cal
Using the formula, we can calculate:
ΔT = (-10,000 cal) / (2000 g x 0.382 cal/g x degrees C)
ΔT ≈ -13.089 degrees C
The change in temperature is -13.089 degrees C, which means the final temperature will be:
Final temperature = Initial temperature - Change in temperature
Final temperature = 95 degrees C - 13.089 degrees C
Final temperature ≈ 81.911 degrees C
Therefore, the final temperature will be approximately 81.911 degrees C after losing 10 kcal of heat from 2000 g of copper initially at 95 degrees C.
1. To calculate the number of calories needed to increase the temperature of copper, you can use the formula:
Q = m * c * ΔT
where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, we have:
m = 50.0 g (mass of copper)
c = 0.382 cal/g x degrees C (specific heat of copper)
ΔT = 75.0 degrees C - 21.0 degrees C (change in temperature)
Plugging in the values into the formula, we can calculate:
Q = 50.0 g * 0.382 cal/g x degrees C * (75.0 degrees C - 21.0 degrees C)
Q = 50.0 g * 0.382 cal/g x degrees C * 54.0 degrees C
Q = 1035.96 cal
Therefore, the number of calories needed to increase the temperature of 50.0 g of copper metal from 21.0 degrees C to 75.0 degrees C is approximately 1036 calories.
2. To find the final temperature when heat is lost from a substance, you can use the formula:
Q = m * c * ΔT
Again, Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. However, in this case, the heat is lost, so the value of Q will be negative.
We have:
m = 2000 g (mass of copper)
c = 0.382 cal/g x degrees C (specific heat of copper)
ΔT = final temperature - initial temperature
Plugging in the values into the formula, we can rearrange it to solve for the final temperature:
-10 kcal = 2000 g * 0.382 cal/g x degrees C * (final temperature - 95 degrees C)
-10000 cal = 2000 g * 0.382 cal/g x degrees C * (final temperature - 95 degrees C)
Dividing through both sides by (2000 g * 0.382 cal/g x degrees C), we get:
(final temperature - 95 degrees C) = -10000 cal / (2000 g * 0.382 cal/g x degrees C)
(final temperature - 95 degrees C) = -26.18 degrees C
Adding 95 degrees C to both sides, we find:
final temperature = 95 degrees C - 26.18 degrees C
final temperature = 68.82 degrees C
Therefore, the final temperature when 2000g of copper at 95 degrees C loses 10kcal of heat is approximately 68.82 degrees C.
q = mass x specific heat x delta T.
Same formula for #2.