the temp of air in a foundry increases when molten metals cool and solidify. Suppose a 45 x 10^6 J of energy is added to the surrounding air by the solidifying metal. The air's temp increases by 55 °C, and the air has a specific heat capacity of 1.0 x 10^3 J/kg x °C. What is the mass of the heated air?
54
c
To find the mass of the heated air, we can use the equation:
Q = mcΔT
Where:
Q = energy added to the air (45 x 10^6 J)
m = mass of the air (unknown)
c = specific heat capacity of air (1.0 x 10^3 J/kg x °C)
ΔT = change in temperature (55 °C)
Rearranging the equation, we get:
m = Q / (c * ΔT)
Substituting the values given:
m = (45 x 10^6 J) / (1.0 x 10^3 J/kg x °C * 55 °C)
Simplifying:
m = (45 x 10^6) / (1.0 x 10^3 * 55)
m = 818.18 kg
Therefore, the mass of the heated air is approximately 818.18 kg.
To calculate the mass of the heated air, we can use the formula:
Q = mcΔT
Where:
Q is the amount of energy transferred to the air (45 x 10^6 J)
m is the mass of the air
c is the specific heat capacity of the air (1.0 x 10^3 J/kg x °C)
ΔT is the change in temperature of the air (55 °C).
Rearranging the formula to solve for mass (m), we have:
m = Q / (c * ΔT)
Substituting the given values, we get:
m = 45 x 10^6 J / (1.0 x 10^3 J/kg x °C * 55 °C)
Simplifying the equation further:
m = 45 x 10^6 J / (55 x 10^3 J/kg)
Canceling out the common unit of energy (J) leaves us with:
m = 45 x 10^6 / 55 x 10^3 kg
Calculating:
m = (45 / 55) x (10^6 / 10^3) kg
m = 0.82 x 10^3 kg
So, the mass of the heated air is approximately 820 kg.