These are Thermodynamics questions:
There is a 7 kg piece of aluminum at 80°C placed in a 3 kg water at 20°C what is the final temperature?
There is a piece of aluminum at 90°C placed in 2 kg of water at 35°C how much energy is transferred if the final temperature is 45? What is the weight of the aluminum?
To solve these thermodynamics questions, we can use the principle of heat transfer, which states that the heat gained by one object is equal to the heat lost by another object in a closed system.
1. **Question 1: Final Temperature**
To find the final temperature when a piece of aluminum and water come into thermal equilibrium, we can use the formula below:
q(aluminum) + q(water) = 0
where q(aluminum) is the heat gained by the aluminum and q(water) is the heat lost by the water.
The heat gained by the aluminum can be calculated as follows:
q(aluminum) = m(aluminum) * c(aluminum) * ΔT(aluminum)
where m(aluminum) is the mass of the aluminum, c(aluminum) is the specific heat capacity of aluminum, and ΔT(aluminum) is the change in temperature of the aluminum.
The heat lost by the water can be calculated as follows:
q(water) = m(water) * c(water) * ΔT(water)
where m(water) is the mass of the water, c(water) is the specific heat capacity of water, and ΔT(water) is the change in temperature of the water.
Since the final temperature is the same for both the aluminum and water, we have:
ΔT(aluminum) = ΔT(water) = T(final) - T(initial)
Given:
m(aluminum) = 7 kg
c(aluminum) = 0.897 J/g°C (specific heat capacity of aluminum)
ΔT(aluminum) = T(final) - 80°C
m(water) = 3 kg
c(water) = 4.18 J/g°C (specific heat capacity of water)
ΔT(water) = T(final) - 20°C
Now, we can substitute the values into the equations and solve them:
m(aluminum) * c(aluminum) * (T(final) - 80) + m(water) * c(water) * (T(final) - 20) = 0
After rearranging the equation, we can solve for T(final).
2. **Question 2: Energy Transferred and Aluminum Weight**
To find out how much energy is transferred when an aluminum piece and water come into thermal equilibrium, we can use the equation:
q = m(aluminum) * c(aluminum) * ΔT(aluminum)
where q is the energy transferred, m(aluminum) is the mass of the aluminum, c(aluminum) is the specific heat capacity of aluminum, and ΔT(aluminum) is the change in temperature of the aluminum.
Given:
m(aluminum) = ? (unknown - what we need to find)
c(aluminum) = 0.897 J/g°C
ΔT(aluminum) = 45°C - 90°C = -45°C (negative sign indicates heat loss)
Now, substitute the values and solve for m(aluminum):
q = m(aluminum) * c(aluminum) * ΔT(aluminum)
Note that if you have the value of q, you can rearrange the equation to solve for m(aluminum) as follows:
m(aluminum) = q / (c(aluminum) * ΔT(aluminum))
Remember to use consistent units for mass (kg) and specific heat capacity (J/g°C or J/kg°C).
I hope this explanation helps you understand how to approach and solve these thermodynamics questions!