A piece of copper is 40g at 200°C is transferred into the copper of calorimeter of mass 60g containing 50g at 25°C what would be the final temperature of the mixture
To find the final temperature of the mixture, we can use the principle of conservation of energy.
The thermal energy gained by the copper piece will be equal to the thermal energy lost by the copper calorimeter and water.
The formula to calculate the thermal energy is:
Q = mcΔT
where:
Q = thermal energy (in Joules)
m = mass (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
First, let's find the thermal energy gained by the copper piece:
Q1 = mcΔT1
m1 = mass of copper piece = 40g
c1 = specific heat capacity of copper = 0.39 J/g°C (approximate value for copper)
ΔT1 = final temperature - initial temperature = final temperature - 200°C
Now, let's find the thermal energy lost by the copper calorimeter and water:
Q2 = mcΔT2
m2 = mass of copper calorimeter and water = mass of copper calorimeter + mass of water = 60g + 50g = 110g
c2 = specific heat capacity of copper calorimeter and water = 4.18 J/g°C (approximate value for water)
ΔT2 = final temperature - initial temperature = final temperature - 25°C
Since the thermal energy gained by the copper piece is equal to the thermal energy lost by the copper calorimeter and water, we can set up the equation:
Q1 = Q2
mcΔT1 = mcΔT2
m1c1ΔT1 = m2c2ΔT2
Substituting the given values:
40g * 0.39 J/g°C * (final temperature - 200°C) = 110g * 4.18 J/g°C * (final temperature - 25°C)
After solving this equation, we can find the value of the final temperature. However, for accurate calculations, it is recommended to use a suitable software or calculator to solve the equation.
To find the final temperature of the mixture, we can use the principle of heat conservation. This principle states that the heat gained by one object is equal to the heat lost by another object during a heat transfer.
Let's break the problem down and calculate the heat gained and lost by each object involved:
1. Heat gained by copper (initial temperature = 200°C, final temperature = T):
The copper gains heat as it transfers from 200°C to a final temperature T. We can calculate this heat using the equation:
Q1 = mcΔT
where Q1 is the heat gained, m is the mass of the copper, c is the specific heat capacity of copper, and ΔT is the change in temperature.
Given that the mass of the copper (m1) is 40g and the change in temperature (ΔT1) is T - 200°C, we can rewrite the equation as:
Q1 = 40g × c × (T - 200)
2. Heat lost by calorimeter (initial temperature = 25°C, final temperature = T):
The calorimeter loses heat as it transfers from 25°C to the final temperature T. We can calculate this heat using the equation:
Q2 = mcΔT
Similar to the previous calculation, Q2 can be expressed as:
Q2 = 60g × c × (T - 25)
3. Heat lost by the water in the calorimeter (initial temperature = 25°C, final temperature = T):
Similar to the calorimeter, we can calculate the heat lost by the water in the calorimeter using the equation:
Q3 = mw × cw × (T - 25)
where mw is the mass of the water (given as 50g) and cw is the specific heat capacity of water.
Since heat gained is equal to heat lost, we can set up an equation:
Q1 + Q2 + Q3 = 0
Now we can substitute the respective equations for Q1, Q2, and Q3 into the equation and solve for T. However, to do this, we need to know the specific heat capacities of copper and water (c and cw).
Once the specific heat capacities are provided, we can solve the equation to find the final temperature (T) of the mixture.