The specific heat of the block is approximately 0.839 J/g°C.
To find the specific heat of the block, we can use the principle of energy conservation.
First, let's calculate the heat gained by the water:
Q of water = mass of water * specific heat of water * change in temperature of water
Where:
- mass of water = 0.217 kg (given)
- specific heat of water = 4.186 J/g°C (specific heat capacity of water)
- change in temperature of water = equilibrium temperature - initial temperature of water
Plugging in the values, we get:
Q of water = 0.217 kg * 4.186 J/g°C * (16.4°C - 25.0°C)
Next, let's calculate the heat lost by the block:
Q of block = mass of block * specific heat of block * change in temperature of block
Where:
- mass of block = 0.350 kg (given)
- specific heat of block = ? (what we're trying to find)
- change in temperature of block = equilibrium temperature - initial temperature of block
Since the block and water come to equilibrium, the heat lost by the block is equal to the heat gained by the water:
Q of block = Q of water
Now we can set up an equation:
mass of block * specific heat of block * change in temperature_block = Q of water
Plugging in the known values, we get:
0.350 kg * specific heat of block * (16.4°C - (-27.5°C)) = Q of water
Simplifying:
0.350 kg * specific heat_block * 43.9°C = Q_water
Since Q of water = 0.217 kg * 4.186 J/g°C * (16.4°C - 25.0°C), we can substitute this value:
0.350 kg * specific heat of block * 43.9°C = 0.217 kg * 4.186 J/g°C * (16.4°C - 25.0°C)
Simplifying further:
specific heat of block = (0.217 kg * 4.186 J/g°C * (16.4°C - 25.0°C)) / (0.350 kg * 43.9°C)
Calculating this expression, we find the specific heat of the block to be approximately:
specific heat_block ≈ 0.839 J/g°C