A 115 g piece of metal, initially at 60.0 °C, is submerged into 100.0 g of water at 25.0 °C. At thermal equilibrium, this mixture had a final temperature of 27.0 °C. The specific heat capacity of water is 4.18 (J/g°C). Use this information to determine the specific heat capacity of the metal (calculate your answer to 3 sig figs).
The heat change for both objects will be equal, so you need two equations and they need to be set to each other. The equation to use is the following:
q=mcT∆
Conditions for 1
m1=mass1=115g
c1=specific heat1=?
T∆1=25.0°C-27.0ºC=-2.0Cº
Conditions for 2:
m2=mass2=100.0g
c2=specific heat2=4.18 (J/g°C)
T∆2=25.0°C-60.ºC=-30.0ºC
m1c1∆T1=m2c2∆T2
(115g)c1(-2.0Cº)=(100.0g)(4.18 (J/g°C))(-30.0ºC)
Solve for c1,
c1=[(100.0g)(4.18 (J/g°C))(-30.0ºC)]/[(115g)(-2.0Cº)]
c1=(-1.25 x 10^4 J/)(-2.3 x 10^2 gºC)
c1=54.3 J/g°C
****I think; I havent had to do this type of calculations in years.
Find the equation of the circle is (3,-2)radius 2 unit
Find the equation of the circle (3,-2), radius 2 unit
To determine the specific heat capacity of the metal, we can use the principle of energy conservation. The heat lost by the metal is equal to the heat gained by the water.
The heat lost by the metal (Q_metal) can be calculated using the formula:
Q_metal = m_metal * c_metal * (T_f - T_initial)
Where:
m_metal is the mass of the metal (115 g)
c_metal is the specific heat capacity of the metal (unknown)
T_f is the final temperature of the mixture (27.0 °C)
T_initial is the initial temperature of the metal (60.0 °C)
The heat gained by the water (Q_water) can be calculated using the formula:
Q_water = m_water * c_water * (T_f - T_water_initial)
Where:
m_water is the mass of the water (100.0 g)
c_water is the specific heat capacity of water (4.18 J/g°C)
T_water_initial is the initial temperature of the water (25.0 °C)
Since the heat lost by the metal is equal to the heat gained by the water at thermal equilibrium, we have:
Q_metal = Q_water
Using the given values, we can now calculate the specific heat capacity of the metal:
115 g * c_metal * (27.0 °C - 60.0 °C) = 100.0 g * 4.18 J/g°C * (27.0 °C - 25.0 °C)
Simplifying the equation:
c_metal * (-33.0 °C) = 100.0 g * 4.18 J/g°C * 2.0 °C
Dividing both sides of the equation by -33.0 °C:
c_metal = (100.0 g * 4.18 J/g°C * 2.0 °C) / (-33.0 °C)
Calculating the specific heat capacity of the metal:
c_metal = -25.3 J/g°C
Rounding to three significant figures:
c_metal = -25.3 J/g°C
Therefore, the specific heat capacity of the metal is approximately -25.3 J/g°C.