if a piece of aluminum with mass 3.99g and a temperature of 100C are dropped into 10cm^3 of water at 21C, what will be the final temperature of the system? The specific heat of aluminium is .900J/gC... ok so i know that i set both equal to each other, but i was wondering do i have to change the 'c' of water to J/gC? please reply and if u have time please please do this and tell me what u get
To find the final temperature of the system, you can use the principle of conservation of energy. The energy lost by the aluminum is equal to the energy gained by the water.
First, convert the mass of aluminum to kilograms:
Mass of aluminum = 3.99g = 0.00399kg
Next, calculate the energy lost by the aluminum:
Energy lost by aluminum = mass of aluminum × specific heat of aluminum × change in temperature
= 0.00399kg × 0.900J/g°C × (final temperature - 100°C)
Now, calculate the energy gained by the water:
Energy gained by water = mass of water × specific heat of water × change in temperature
= 10cm³ × 1g/cm³ × 4.18J/g°C × (final temperature - 21°C)
Since energy lost by the aluminum is equal to the energy gained by the water, we can set these equations equal to each other:
0.00399kg × 0.900J/g°C × (final temperature - 100°C) = 10cm³ × 1g/cm³ × 4.18J/g°C × (final temperature - 21°C)
You don't need to convert the specific heat of water to joules per gram-degree Celsius because both sides of the equation are already in grams.
Now, let's calculate the final temperature:
0.00399kg × 0.900J/g°C × final temperature - 0.00399kg × 0.900J/g°C × 100°C = 10cm³ × 1g/cm³ × 4.18J/g°C × final temperature - 10cm³ × 1g/cm³ × 4.18J/g°C × 21°C
0.00399kg × 0.900J/g°C × final temperature - 0.00399kg × 0.900J/g°C × 100°C = 10cm³ × 1g/cm³ × 4.18J/g°C × final temperature - 10cm³ × 1g/cm³ × 4.18J/g°C × 21°C
0.00359J/°C × final temperature - 0.359J/°C = 41.8J/°C × final temperature - 87.78J/°C
Now, let's simplify the equation:
0.00359J/°C × final temperature - 41.8J/°C × final temperature = 0.359J/°C - 87.78J/°C
-38.21J/°C × final temperature = -87.421J/°C
Finally, solve for the final temperature:
final temperature = -87.421J/°C / -38.21J/°C
final temperature = 2.286°C
Therefore, the final temperature of the system will be approximately 2.286°C.
To find the final temperature of the system, you need to apply the principle of energy conservation, which states that the heat lost by one object is equal to the heat gained by another object in a closed system.
First, calculate the heat lost by the piece of aluminum using the formula:
Q = m * c * ΔT
Where:
Q = heat lost
m = mass of aluminum (in grams)
c = specific heat capacity of aluminum (in J/g°C)
ΔT = change in temperature of aluminum
Given:
m = 3.99g
c = 0.900 J/g°C
Initial temperature of aluminum = 100°C
Final temperature of aluminum = ?
ΔT = Final temperature - Initial temperature = Final temperature - 100°C
Next, calculate the heat gained by the water using the formula:
Q = m * c * ΔT
Where:
Q = heat gained
m = mass of water (in grams)
c = specific heat capacity of water (in J/g°C)
ΔT = change in temperature of water
Given:
m = 10 cm³ (since 1 cm³ of water is equal to 1 gram)
c = 4.184 J/g°C (specific heat capacity of water)
Initial temperature of water = 21°C
Final temperature of water = ?
ΔT = Final temperature - Initial temperature = Final temperature - 21°C
Now, since the heat lost by the aluminum is equal to the heat gained by the water, we can set up the equation:
m_aluminum * c_aluminum * (Final temperature - 100°C) = m_water * c_water * (Final temperature - 21°C)
Plugging in the known values:
(3.99 g) * (0.900 J/g°C) * (Final temperature - 100°C) = (10 g) * (4.184 J/g°C) * (Final temperature - 21°C)
Simplifying the equation, we can cancel out the units of grams and °C:
(3.99 * 0.900) * (Final temperature - 100) = (10 * 4.184) * (Final temperature - 21)
Now, we can solve for the Final temperature of the system by isolating the variable:
(3.591) * (Final temperature - 100) = (41.84) * (Final temperature - 21)
Expand the equation:
3.591 * Final temperature - 359.1 = 41.84 * Final temperature - 876.64
Rearrange the equation:
3.591 * Final temperature - 41.84 * Final temperature = -876.64 + 359.1
Combine like terms:
-38.249 * Final temperature = -517.54
Divide both sides by -38.249:
Final temperature = -517.54 / -38.249
Final temperature ≈ 13.53°C (rounded to two decimal places)
Therefore, the final temperature of the system is approximately 13.53°C.