in a vessel of 40 cm3 of water at 4 ° C is introduced aluminum over 80g to 8 º C. neglecting the effect of the vessel, calculate final temperature
"over 80g to 8º C" does not make sense.
Do you mean ".. is introduced 80 g of aluminum 80g at 8 ºC" ?
If so, equate the heat loss of the Al to the heat gain of the water, and solve for the unknown final T. You will need the specific heat of aluminum.
To calculate the final temperature, we can use the principle of conservation of energy. The energy gained by the aluminum is equal to the energy lost by the water. The formula to calculate this is:
Q_aluminum = Q_water
where Q_aluminum is the energy gained by aluminum and Q_water is the energy lost by water.
The energy gained or lost by an object can be calculated using the formula:
Q = m * c * ΔT
where Q is the energy gained or lost, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature.
Given that the mass of the water is 40 cm^3 and the mass of the aluminum is 80g, we need to convert the volume of water to mass by using its density:
Density of water = 1 g/cm^3
Mass of water = Volume of water * Density of water
= 40 cm^3 * 1 g/cm^3
= 40 g
Now, we can calculate the energy gained by aluminum and the energy lost by water.
Q_aluminum = m_aluminum * c_aluminum * ΔT_aluminum
= 80g * c_aluminum * (Final temperature - 8 °C)
Q_water = m_water * c_water * ΔT_water
= 40g * c_water * (Final temperature - 4 °C)
Since Q_aluminum = Q_water, we can equate the two expressions:
80g * c_aluminum * (Final temperature - 8 °C) = 40g * c_water * (Final temperature - 4 °C)
Now, we have an equation with one variable (Final temperature). We can solve for Final temperature by rearranging the equation and solving for it.
(80g * c_aluminum * Final temperature) - (80g * c_aluminum * 8 °C) = (40g * c_water * Final temperature) - (40g * c_water * 4 °C)
80g * c_aluminum * Final temperature - 40g * c_water * Final temperature = 40g * c_water * 4 °C - 80g * c_aluminum * 8 °C
Final temperature * (80g * c_aluminum - 40g * c_water) = 40g * c_water * 4 °C - 80g * c_aluminum * 8 °C
Final temperature = (40g * c_water * 4 °C - 80g * c_aluminum * 8 °C) / (80g * c_aluminum - 40g * c_water)
Substituting the specific heat capacities for aluminum and water, which are approximately 0.897 J/g°C and 4.18 J/g°C respectively, into the equation, we can calculate the final temperature.