A brass rod of 0.2 kg at 100degree Celsius is dropped into 0.5 kg of water at 20 degree Celsius. The final temperature of the mixture is 23 degree Celsius.calculate the specific heat capacity of brass(specific heat capacity of Water is 4200 j/kg degree c
To determine the specific heat capacity of brass, we need to use the principle of heat exchange. The heat lost by the brass rod is equal to the heat gained by the water in the final temperature.
The heat lost by the brass rod can be calculated using the formula:
Q = mcΔt,
where Q is the heat lost, m is the mass of the brass rod, c is the specific heat capacity of brass, and Δt is the change in temperature.
The heat gained by the water can be calculated using the formula:
Q = mcΔt,
where Q is the heat gained, m is the mass of the water, c is the specific heat capacity of water, and Δt is the change in temperature.
In this case, we assume no heat is lost to the surroundings.
Given:
Mass of brass rod (m1) = 0.2 kg
Initial temperature of brass rod (T1) = 100°C
Mass of water (m2) = 0.5 kg
Initial temperature of water (T2) = 20°C
Final temperature (Tf) = 23°C
Specific heat capacity of water (c2) = 4200 J/kg°C
First, we need to calculate the change in temperature for both the brass rod and the water:
Change in temperature of brass rod (Δt1) = Tf - T1
Change in temperature of water (Δt2) = Tf - T2
Next, we can calculate the heat lost by the brass rod using the formula:
Q1 = m1 * c1 * Δt1
Similarly, we can calculate the heat gained by the water using the formula:
Q2 = m2 * c2 * Δt2
Since the heat lost by the brass rod is equal to the heat gained by the water, we can set up an equation:
Q1 = Q2
Substituting the values we know:
m1 * c1 * Δt1 = m2 * c2 * Δt2
Solving for the specific heat capacity of brass (c1):
c1 = (m2 * c2 * Δt2) / (m1 * Δt1)
Plugging in the values:
c1 = (0.5 kg * 4200 J/kg°C * (23°C - 20°C)) / (0.2 kg * (23°C - 100°C))
Now, we can simplify and solve this equation to find the specific heat capacity of brass.