A 0.250-kg block of a pure material is heated from 20.0°C to 65.0°C by the addition of 4.35 kJ of energy. Calculate its specific heat and identify the substance of which it is most likely composed.
387
313J/kgC
To calculate the specific heat of the material, we can use the formula:
q = mcΔT
where:
q is the amount of heat transferred (in Joules),
m is the mass of the object (in kg),
c is the specific heat of the material (in J/(kg·°C)),
and ΔT is the change in temperature (in °C).
In this case, we know the following values:
m = 0.250 kg
ΔT = 65.0°C - 20.0°C = 45.0°C = 45.0 K
q = 4.35 kJ = 4.35 × 10³ J (since 1 kJ = 10³ J)
Rearranging the formula, we get:
c = q / (mΔT)
Substituting the given values:
c = 4.35 × 10³ J / (0.250 kg × 45.0 K)
c ≈ 193.3 J/(kg·K)
The specific heat of the material is approximately 193.3 J/(kg·K).
Next, we can use the known values for specific heat to identify the substance. Different substances have different specific heat values. By comparing the specific heat value we calculated (193.3 J/(kg·K)) to known specific heat values for different substances, we can determine the substance it is most likely composed of.
For example, the specific heat of water is approximately 4180 J/(kg·K), which is significantly higher than the value we calculated. This suggests that the block is not composed of water.
Some common substances and their specific heat values include:
- Aluminum: 900 J/(kg·K)
- Copper: 385 J/(kg·K)
- Iron: 449 J/(kg·K)
- Lead: 128 J/(kg·K)
- Silver: 235 J/(kg·K)
- Gold: 129 J/(kg·K)
Based on these values, it is most likely that the block of pure material is composed of either lead or gold, as their specific heat values are in the closest range to the calculated value of 193.3 J/(kg·K).
To calculate the specific heat of a substance and identify the material it is composed of, we can use the formula:
q = mcΔT
Where:
q = heat energy
m = mass
c = specific heat capacity
ΔT = change in temperature
We are given:
Mass (m) = 0.250 kg
Initial Temperature (T1) = 20.0°C
Final Temperature (T2) = 65.0°C
Heat Energy (q) = 4.35 kJ = 4.35 × 10^3 J
First, let's calculate the change in temperature (ΔT):
ΔT = T2 - T1
= 65.0°C - 20.0°C
= 45.0°C
Now, we can rearrange the equation to solve for the specific heat capacity (c):
c = q / (m * ΔT)
Substituting the given values:
c = (4.35 × 10^3 J) / (0.250 kg * 45.0°C)
Calculating the specific heat capacity:
c = (4.35 × 10^3 J) / (11.25°C)
c ≈ 386.67 J/kg°C
The specific heat capacity is approximately 386.67 J/kg°C.
Now, we need to identify the material based on its specific heat capacity. We can compare this value to known specific heat capacities of different substances. Here are the specific heat capacities of some common substances:
- Water: 4186 J/kg°C
- Aluminum: 900 J/kg°C
- Iron: 448 J/kg°C
- Copper: 386 J/kg°C
- Lead: 128 J/kg°C
Based on the specific heat capacity of approximately 386.67 J/kg°C, the substance is most likely composed of copper, as it has a similar specific heat capacity.