A metal sample weighing 45.0 g and at a temperature of 99.1 degrees Celsius was placed in 38.6 g of water in a calorimeter at 25.0 degrees Celsius. The calorimeter reached a maximum temperature of 32.8 degrees Celsius. what was the delta t of water? what was delta t of metal? how much heat flowed into the water?
To calculate the values you mentioned, we need to use the formula for heat transfer:
q = m * c * ΔT
where:
q represents the heat flow (in joules),
m represents the mass (in grams),
c represents the specific heat capacity (in J/g°C), and
ΔT represents the change in temperature (in °C).
First, let's calculate the ΔT of the water:
m_water = 38.6 g (mass of water)
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT_water = T_final - T_initial
= 32.8°C - 25.0°C
= 7.8°C
ΔT_water = 7.8°C
Next, let's calculate the ΔT of the metal:
m_metal = 45.0 g (mass of the metal)
ΔT_metal = T_final - T_initial
= 32.8°C - 99.1°C
= -66.3°C
ΔT_metal = -66.3°C
Now, let's calculate the heat flow (q) into the water:
q_water = m_water * c_water * ΔT_water
Substituting the values we have:
q_water = 38.6 g * 4.18 J/g°C * 7.8°C
q_water = 1234.404 J
Therefore, the amount of heat that flowed into the water is 1234.404 J.
To summarize:
- ΔT of water (ΔT_water) = 7.8°C
- ΔT of metal (ΔT_metal) = -66.3°C
- Heat flowed into the water (q_water) = 1234.404 J
To calculate the delta t (change in temperature) of the water, we can subtract the initial temperature from the final temperature:
Delta t of water = Final temperature - Initial temperature
Delta t of water = 32.8°C - 25.0°C
Delta t of water = 7.8°C
The delta t (change in temperature) of the metal can be calculated in the same way:
Delta t of metal = Final temperature - Initial temperature
Delta t of metal = 32.8°C - 99.1°C
Delta t of metal = -66.3°C (Note: the negative sign indicates a decrease in temperature.)
To calculate the amount of heat that flowed into the water, we can use the specific heat capacity formula:
Heat energy = Mass * Specific heat capacity * Delta t
Given data:
- Mass of water (m1) = 38.6 g
- Delta t of water = 7.8°C
- Specific heat capacity of water (c1) = 4.18 J/g°C
Heat flowed into the water = m1 * c1 * Delta t of water
Heat flowed into the water = 38.6 g * 4.18 J/g°C * 7.8°C
Heat flowed into the water ≈ 1193.53 J (or 1.19 kJ)
Therefore, the delta t of water is 7.8°C, the delta t of the metal is -66.3°C, and approximately 1.19 kJ of heat flowed into the water.