To find the mass ( m ) of the substance given the temperatures ( t_1 ) and ( t_2 ), the heat transfer ( Q ), and the specific heat capacity ( c ), you can use the formula for heat transfer:
[
Q = m \cdot c \cdot \Delta t
]
where:
- ( Q ) is the heat transfer (in joules),
- ( m ) is the mass (in kilograms),
- ( c ) is the specific heat capacity (in joules per kilogram per degree Celsius),
- ( \Delta t ) is the change in temperature (in degrees Celsius).
First, calculate the change in temperature ( \Delta t ):
[
\Delta t = t_1 - t_2 = 400^\circ C - 210^\circ C = 190^\circ C
]
Now substitute the known values into the formula:
[
14500 , \text{J} = m \cdot 380 , \text{J/(kg}\cdot^\circ C) \cdot 190 , ^\circ C
]
Now simplify the equation:
[
14500 = m \cdot 380 \cdot 190
]
Calculate ( 380 \cdot 190 ):
[
380 \cdot 190 = 72200
]
So the equation is now:
[
14500 = m \cdot 72200
]
Now, solve for ( m ):
[
m = \frac{14500}{72200} \approx 0.2005 , \text{kg}
]
Thus, the mass ( m ) is approximately ( 0.2005 , \text{kg} ) or about ( 200.5 , \text{g} ).
