Please Help!
An object at 20 degrees Celsius with heat capacity 100 calories/Celsius is placed in 40 grams of water at 100 degrees Celsius. After equilibrium is reached, the object is removed from the hot water and placed in 200 grams of water at 0 degrees Celsius. What is the final temperature of the object? Explain.
Thanks for the help!
This question was answered yesterday. See the links below. At least one will have my answer.
To find the final temperature of the object, we need to understand the concept of heat transfer and the principle of conservation of energy.
We know that heat is transferred from the object to the water until thermal equilibrium is reached. The heat transfer can be calculated using the formula:
Q = m * c * ΔT
where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Let's calculate the heat transferred when the object is placed in the hot water:
Q1 = m1 * c1 * ΔT1
Given:
m1 (mass of hot water) = 40 grams
c1 (specific heat capacity of water) = 1 calorie/gram°C
ΔT1 (change in temperature) = final temperature of the object - initial temperature of the hot water
Now, we need to calculate the heat transferred when the object is placed in the cold water:
Q2 = m2 * c2 * ΔT2
Given:
m2 (mass of cold water) = 200 grams
c2 (specific heat capacity of water) = 1 calorie/gram°C
ΔT2 (change in temperature) = final temperature of the object - initial temperature of the cold water
Since heat is conserved, the total heat transferred from the object to the water in both cases is equal:
Q1 + Q2 = 0
Substituting the formulas for Q1 and Q2:
m1 * c1 * ΔT1 + m2 * c2 * ΔT2 = 0
Rearranging the equation:
ΔT1 = - (m2 * c2 * ΔT2) / (m1 * c1)
Now, let's substitute the given values into the equation:
m1 = 40 grams
c1 = 100 calories/Celsius
ΔT1 = final temperature of the object - 100 degrees Celsius
m2 = 200 grams
c2 = 1 calorie/gram°C
ΔT2 = 0 degrees Celsius - final temperature of the object
After substituting the values, we can solve the equation to find the final temperature of the object.