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Answer :
1) the specific heat of the metal is approximately 0.39 J/g°C.
2) the final temperature of the metal is approximately 36.19°C.
1. The specific heat of a substance is a measure of how much heat energy is required to raise the temperature of 1 gram of that substance by 1 degree Celsius.
To find the specific heat of the metal in this question, we can use the formula:
q = mcΔT
where q is the heat energy absorbed or released, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature. In this case, the metal sample is heated and then placed in water.
The heat energy gained by the water can be calculated using the formula:
q_water = mc_waterΔT_water
where q_water is the heat energy gained by the water, m_water is the mass of the water, c_water is the specific heat of water, and ΔT_water is the change in temperature of the water.
Since the heat gained by the water is equal to the heat lost by the metal, we can set up the equation: q_water = -q_metal
Plugging in the given values, we have: mc_waterΔT_water = -mc_metalΔT_metal
Rearranging the equation, we get:
c_metal = - (mc_waterΔT_water) / (m_metalΔT_metal)
Plugging in the given values and solving the equation, we find:
c_metal = - (97.4g * 4.184 J/g°C * (27.2°C - 22.74°C)) / (62.3g * (83.25°C - 22.74°C))
c_metal ≈ 0.39 J/g°C (rounded to 2 decimal places)
So, the specific heat of the metal is approximately 0.39 J/g°C.
2. In this question, we are given the initial temperature, mass, and specific heat of the metal, as well as the amount of heat energy it gives off to the surroundings.
We need to find the final temperature of the metal. We can use the formula:
q = mcΔT
where q is the heat energy absorbed or released, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.
In this case, the metal is giving off heat energy to the surroundings, so the value of q will be negative. We can rearrange the formula to solve for the change in temperature:
ΔT = q / (mc)
Plugging in the given values, we have:
ΔT = -38 J / (45.05g * 0.394 J/g°C) ΔT ≈ -0.216°C
Since the initial temperature of the metal is 36.41°C, the final temperature can be found by subtracting the change in temperature:
Final temperature = Initial temperature + ΔT
Final temperature ≈ 36.41°C - 0.216°C
Final temperature ≈ 36.19°C
So, the final temperature of the metal is approximately 36.19°C.
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