The temperature difference between the inlet and the outlet of an air-cooled engine is 30.0K. The engine generates 7.0kW of waste power that the air extracts from the engine. Calculate the rate of flow of air (in kg s^-1) needed to extract this power?
SPECIFIC HEAT CAPACITY of air (at constant pressure)= 1.01 x10^3J kg^-1 K^-1
power extracted=airmass/sec*heatcapacity*tempdifference.
solve for air mass rate
= power extracted/(heatcap*tempdiff)
Q=Power * time
m= Q/shc*temp change
To calculate the rate of flow of air needed to extract the waste power, we can use the equation:
rate of flow of air (m) = waste power (P) / (temperature difference (ΔT) x specific heat capacity of air (c))
Plugging in the given values:
waste power (P) = 7.0 kW = 7.0 x 10^3 W
temperature difference (ΔT) = 30.0 K
specific heat capacity of air (c) = 1.01 x 10^3 J kg^-1 K^-1
We first need to convert the waste power from kilowatts to watts:
waste power (P) = 7.0 x 10^3 W
Now we can plug the values into the equation to calculate the rate of flow of air:
rate of flow of air (m) = (7.0 x 10^3) / (30.0 x 1.01 x 10^3)
Simplifying the expression:
rate of flow of air (m) = 0.23 kg s^-1
Therefore, the rate of flow of air needed to extract the waste power is 0.23 kg s^-1.
To calculate the rate of flow of air needed to extract the waste power from the engine, we can use the formula:
Power = mass flow rate * specific heat capacity * temperature difference
Here, we know the waste power generated by the engine is 7.0 kW, the specific heat capacity of air is 1.01 x 10^3 J kg^-1 K^-1, and the temperature difference is 30.0 K.
1. Convert the power to SI unit:
7.0 kW = 7.0 x 10^3 W
2. Rearrange the formula to solve for the mass flow rate:
mass flow rate = power / (specific heat capacity * temperature difference)
3. Substitute the values into the formula:
mass flow rate = (7.0 x 10^3) / (1.01 x 10^3 * 30.0)
4. Calculate the mass flow rate:
mass flow rate ≈ 0.232 kg/s
Therefore, the rate of flow of air needed to extract the power from the engine is approximately 0.232 kg/s.