Thermal energy question
A 40.0kg sample of concrete has 10% zinc impurity (by mass). If 6.0x10^4J of thermal energy is added to the sample, determine the change in temperature.
m₁=36 kg, c₁= 880 J/kg•K,
m₂=4 kg, c₂=387 J/kg•K
Q=m₁c₁ΔT + m₂c₂ΔT =
= ΔT(m₁c₁ + m₂c₂).
ΔT= Q/(m₁c₁ + m₂c₂)=
=60000/(36•880+4•387) = 1.8 K
To determine the change in temperature, we need to use the specific heat capacity (represented by the symbol "c") of the material. The specific heat capacity is the amount of thermal energy required to change the temperature of a certain mass of a substance by 1 degree Celsius.
The equation for calculating the change in temperature is:
Q = mcΔT
Where:
- Q is the thermal energy added to the sample (6.0x10^4 J in this case)
- m is the mass of the sample (40.0 kg)
- c is the specific heat capacity of the material (we will assume it is for concrete, which is approximately 879 J/kg°C)
- ΔT is the change in temperature that we are trying to find.
First, we need to calculate the mass of the zinc impurity in the concrete sample by multiplying the mass of the sample (40.0 kg) by the percentage of zinc impurity (10% = 0.10):
Mass of zinc impurity = 40.0 kg x 0.10 = 4.0 kg
Next, we need to calculate the mass of the pure concrete by subtracting the mass of the zinc impurity from the total mass of the sample:
Mass of pure concrete = Mass of sample - Mass of zinc impurity
= 40.0 kg - 4.0 kg
= 36.0 kg
Now, we can calculate the change in temperature using the equation mentioned earlier:
Q = mcΔT
Rearranging the equation to solve for ΔT:
ΔT = Q / mc
Substituting the values:
ΔT = (6.0x10^4 J) / (36.0 kg x 879 J/kg°C)
Calculating the value:
ΔT ≈ 1.70°C
Therefore, the change in temperature is approximately 1.70°C.