Hi! Help me please, thank you so much.
What mass of water at 28.0 °C must be allowed to come to thermal equilibrium with a 2.05-kg cube of aluminum initially at 1.50 102 °C to lower the temperature of the aluminum to 54.8 °C? Assume any water turned to stream subsequently recondenses.
The sum of the heats GAINED is zero. (one will have a negative heat gained).
Heatgainedwater+heatgainedAl=0
mass*cw*(Tf-28)+2.05kg*Cal(Tf-tial)=0
put in the specific heat constants, Tfinal, and solve for mass.
To find the mass of water required to lower the temperature of the aluminum cube, we can use the principle of thermal equilibrium. This principle states that when two objects are in contact, heat will flow from the hotter object to the colder object until they reach the same temperature.
We can calculate the amount of heat transferred (Q) using the formula:
Q = m1 * c1 * ΔT1
where:
m1 is the mass of the aluminum cube (2.05 kg)
c1 is the specific heat capacity of aluminum (0.90 J/g°C)
ΔT1 is the change in temperature of the aluminum (final temperature - initial temperature)
Let's calculate Q:
ΔT1 = 54.8°C - 102°C = -47.2°C (note that we take the negative value because the temperature of the aluminum is decreasing)
Q = 2.05 kg * 0.90 J/g°C * (-47.2°C) = -89.848 J
Since heat is transferred from the aluminum to the water, the amount of heat gained by the water (Q) will be equal to the amount of heat lost by the aluminum. This can be written as:
Q = m2 * c2 * ΔT2
where:
m2 is the mass of the water we need to find
c2 is the specific heat capacity of water (4.18 J/g°C)
ΔT2 is the change in temperature of the water (final temperature - initial temperature)
We can rearrange the equation to solve for m2:
m2 = Q / (c2 * ΔT2)
Let's calculate m2:
ΔT2 = 28.0°C - 54.8°C = -26.8°C
m2 = -89.848 J / (4.18 J/g°C * (-26.8°C))
Note that we are using the negative value for ΔT2 because the temperature of the water is also decreasing.
Calculating the value, we find:
m2 = 5.400 g
Therefore, approximately 5.400 grams of water at 28.0 °C must be allowed to come to thermal equilibrium with the aluminum cube to lower its temperature to 54.8 °C.