A cube of gold weighing 192.4g is heated from 30.0°C to some higher temperature, with the absorption of 226 joules of heat. The specific heat of gold is 0.030 J/g∙°C. What was the final temperature of the gold?
The specific heat formula is given as:
Q = mcΔT
where:
Q = heat energy absorbed by the object (in joules)
m = mass of the object (in grams)
c = specific heat capacity of the object (in J/g∙°C)
ΔT = change in temperature (in °C)
Given:
Q = 226 J
m = 192.4 g
c = 0.030 J/g∙°C
Let's first calculate the change in temperature using the formula:
ΔT = Q / (mc)
ΔT = 226 J / (192.4 g * 0.030 J/g∙°C)
ΔT = 226 J / 5.772 g∙°C
ΔT ≈ 39.162 °C
Now, let's find the final temperature by adding the change in temperature to the initial temperature (30.0°C):
Final Temperature = Initial Temperature + ΔT
Final Temperature = 30.0°C + 39.162 °C
Final Temperature ≈ 69.162 °C
Therefore, the final temperature of the gold cube is approximately 69.162 °C.
To find the final temperature of the gold cube, we can use the formula for heat:
Q = mcΔT
Where:
Q = heat absorbed (226 J)
m = mass of the gold cube (192.4 g)
c = specific heat of gold (0.030 J/g∙°C)
ΔT = change in temperature (final temperature - initial temperature)
We need to rearrange the formula to solve for the final temperature.
ΔT = Q / (mc)
Now, we can plug in the known values:
ΔT = 226 J / (192.4 g * 0.030 J/g∙°C)
ΔT = 226 J / 5.772 g∙°C
ΔT ≈ 39.184 °C (rounded to three decimal places)
Since ΔT represents the change in temperature, the final temperature can be found by adding ΔT to the initial temperature:
Final temperature = 30.0 °C + ΔT
Final temperature = 30.0 °C + 39.184 °C
Final temperature ≈ 69.184 °C (rounded to three decimal places)
Therefore, the final temperature of the gold cube is approximately 69.184 °C.
To find the final temperature of the gold cube, we can use the equation:
Q = mcΔT
where Q is the heat absorbed by the cube, m is the mass of the cube, c is the specific heat of gold, and ΔT is the change in temperature.
Given:
- Mass of the cube (m) = 192.4g
- Heat absorbed (Q) = 226 Joules
- Specific heat of gold (c) = 0.030 J/g∙°C
We need to find ΔT, which is the change in temperature.
We can rearrange the equation to solve for ΔT:
ΔT = Q / (mc)
Substituting the given values, we have:
ΔT = 226 J / (192.4g * 0.030 J/g∙°C)
Now we can calculate ΔT:
ΔT = 226 J / (5.772 g∙°C)
ΔT ≈ 39.18 °C
Finally, to find the final temperature, we add the change in temperature (ΔT) to the initial temperature:
Final Temperature = Initial Temperature + ΔT
Given that the initial temperature is 30.0°C:
Final Temperature = 30.0°C + 39.18°C
Therefore, the final temperature of the gold cube is approximately 69.18°C.