Conventional engines ignite their fuel by using the spark from the spark plug. But in a diesel engine, the air enthers the chamber at the temperature of the atmosphere and is compressed by the piston until it reaches 550 degrees Celsius, at which time the fuel is injected itno the chamber and ignited by the hot air. There is no spark plug and no heat is put into the air. (One of the drawbacks of diesel engines is that they are hard to start in cold weather) Suppose a certain chamber has a maximum volume of .5 L and uses .05 mole of air. we can model the air as all ideal N2 and use the appropriate values from Table 15.4 (a) If the air temperature is 20 degrees Celsius what is the colume of the air (which started at .5 L) when it has been compressed enough so that its temperature has risen to 550 degrees celsius? (b) What is the change in internal energy of the air during this compression? (c) How much work did the piston do on this gas while compressing it? (d) Suppose it is cold winter morning, with air temperature 10 degrees Farenheit. If the piston compressed the air by the same amount as before, what will be the highest temperature the gas will reach in this case? (e) DO you now see why a diesel engine is hard to start in cold weather? Can you suggest any reasonable technological solutions to help start a diesel engine on a cold day?
(a) To find the volume of the air when its temperature has risen to 550 degrees Celsius, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (assumed to be constant)
V = volume
n = number of moles of air
R = gas constant
T = temperature
Let's assume the pressure remains constant. Rearranging the equation, we get:
V1 / T1 = V2 / T2
V1 = initial volume = 0.5 L
T1 = initial temperature = 20 degrees Celsius + 273 = 293 K
T2 = final temperature = 550 degrees Celsius + 273 = 823 K
Plugging these values into the equation, we can solve for V2:
V2 = (V1 * T2) / T1
V2 = (0.5 * 823) / 293
V2 ≈ 1.406 L
Therefore, the volume of the air when its temperature has risen to 550 degrees Celsius is approximately 1.406 L.
(b) The change in internal energy (ΔU) during compression can be calculated using the equation:
ΔU = (3/2) * n * R * ΔT
Where:
ΔU = change in internal energy
n = number of moles of air
R = gas constant
ΔT = change in temperature = T2 - T1
Substituting the values:
ΔT = 823 K - 293 K = 530 K
ΔU = (3/2) * 0.05 * 8.314 * 530
ΔU ≈ 311.32 J
Therefore, the change in internal energy of the air during compression is approximately 311.32 J.
(c) The work done by the piston on the gas during compression can be calculated using the equation:
W = ΔU - Q
Where:
W = work done
ΔU = change in internal energy (which we calculated in part b)
Q = heat transferred to or from the system (since no heat is transferred in this case, Q = 0)
Therefore, the work done by the piston on the gas while compressing it is equal to the change in internal energy, which is approximately 311.32 J.
(d) To calculate the highest temperature the gas will reach in colder weather, we can follow a similar approach as part a.
V1 = initial volume = 0.5 L
T1 = initial temperature = 10 degrees Fahrenheit + 459.67 = 469.67 K
T2 = final temperature (unknown)
Using the equation V1 / T1 = V2 / T2, we can solve for T2:
T2 = (V2 * T1) / V1
T2 = (0.5 * 823) / 469.67
T2 ≈ 0.878 K
Therefore, the highest temperature the gas will reach in this case is approximately 0.878 K.
(e) The reason why a diesel engine is hard to start in cold weather is because the air entering the combustion chamber is colder, which results in lower temperatures during compression. Diesel engines rely on the heat generated by compressing the air to ignite the fuel, and if the air is too cold, it may not reach the required temperature for combustion.
Some possible technological solutions to help start a diesel engine on a cold day include:
1. Glow plugs: These are electric heating elements installed in the combustion chamber that preheat the air before starting the engine. They provide additional heat during cold starts to ensure proper ignition.
2. Block heaters: These are electric heating devices that warm the engine block before starting. They can be plugged into an electrical outlet, providing heat to the engine and facilitating easier starts in cold weather.
3. Fuel additives: Specialized additives can be added to the diesel fuel to lower its freezing point, making it less susceptible to solidifying in cold temperatures.
4. Engine coolant heaters: These are devices that warm the engine coolant before starting, helping to warm the engine and facilitate easier starts.
These solutions help to provide additional heat or preheat crucial components of the engine, ensuring that the air reaches an adequate temperature for combustion even in cold weather conditions.