A water-cooled engine produces 1589 W of power. Water enters the engine block at 14.61 °C and exits at 29.91 °C. The rate of water flow is 147.3 L/h. What is the engine’s efficiency?
You know that the mechanical power out is
W = 1589 J/s
The mass flow rate of coolant is
dm/dt = 147.3 l/h = (147.3L/h*10^3 g/L)/3600s/h
= 40.9 g/s
The heat energy (rate) out to the cooling water is
Qout = C*(dm/dt)*deltaT
= 4.18 J/(°C*g)*40.9 g/s *15.3 °C
= 2617 J/s
The heat energy rate in = Qout + Wout
= 2617 + 1589 = 4206 J/s
Efficiency = Wout/(Qin) = 1589/4206 = 37.8%
To calculate the engine's efficiency, we need to determine the amount of heat transferred from the engine to the cooling water and compare it to the amount of power the engine produces.
First, we need to find the heat transferred from the engine to the cooling water. We can use the specific heat capacity of water to calculate this.
The formula for calculating the heat transferred is:
Q = mcΔT
where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
To find the mass of water (m), we need to convert the rate of water flow from liters per hour to kilograms per second.
1 liter of water is equal to 1 kilogram, and 1 hour is equal to 3600 seconds.
Therefore, the mass flow rate of water (ṁ) is:
ṁ = (147.3 L/h) x (1 kg/L) / (3600 s/h)
Next, we need to calculate the change in temperature (ΔT) using the given values:
ΔT = (29.91 °C) - (14.61 °C)
Now, we can substitute the values into the formula to find the heat transferred (Q):
Q = ṁcΔT
Next, we need to calculate the power produced by the engine and convert it to joules per second (Watts). The given power is already in Watts, so we can directly use it.
Now, we can calculate the engine's efficiency using the formula:
Efficiency = (output power / input power) x 100%
In this case, the output power is the power produced by the engine, and the input power is the heat transferred from the engine to the cooling water.
Let's calculate the values step by step:
1. Convert the rate of water flow to kg/s:
ṁ = (147.3 L/h) x (1 kg/L) / (3600 s/h)
2. Calculate the change in temperature:
ΔT = (29.91 °C) - (14.61 °C)
3. Calculate the heat transferred:
Q = ṁcΔT
4. Calculate the engine's efficiency:
Efficiency = (output power / input power) x 100%
By following these steps, you can find the engine's efficiency.