If 200 cm3 of tea at 95°C is poured into a 150-g glass cup initially at 25°C, what will be the common final temperature T of the tea and cup when equilibrium is reached, assuming no heat flows to the surroundings
pls how can I solve this should the 200cm cube be convert to mass and how?
how can i answer this question?
How to solve it?
First convert it to g
To find the common final temperature (T) of the tea and cup when equilibrium is reached, we need to use the principle of conservation of energy.
The heat gained by the tea and cup must equal the heat lost by the tea and cup.
Let's first determine the heat gained by the tea. We can use the formula:
Q = mcΔT
Where:
Q = heat energy gained
m = mass of the tea (200 g, assuming water density of 1.0 g/cm3)
c = specific heat capacity of water (4.18 J/g°C, approximately)
ΔT = change in temperature
The change in temperature of the tea can be calculated as:
ΔT = T - 95°C
Substituting the given values into the formula, we have:
Qtea = (200 g) × (4.18 J/g°C) × (T - 95°C)
Now, let's determine the heat gained by the cup. We can use the formula:
Q = mcΔT
Where:
Q = heat energy gained
m = mass of the cup (150 g)
c = specific heat capacity of glass (0.84 J/g°C, approximately)
ΔT = change in temperature
The change in temperature of the cup can be calculated as:
ΔT = T - 25°C
Substituting the given values into the formula, we have:
Qcup = (150 g) × (0.84 J/g°C) × (T - 25°C)
Since there is no heat flow to the surroundings, the heat gained by the cup and the tea must be equal:
Qtea = Qcup
Therefore, we can set up the equation:
(200 g) × (4.18 J/g°C) × (T - 95°C) = (150 g) × (0.84 J/g°C) × (T - 25°C)
Now, solve this equation for T to find the common final temperature.