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?
To answer these questions, we can use the ideal gas law and the first law of thermodynamics.
(a) To find the volume of the air after compression, we need to calculate the final temperature and use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Given:
Initial volume (V1) = 0.5 L
Initial temperature (T1) = 20 degrees Celsius = 293 K
Final temperature (T2) = 550 degrees Celsius = 823 K
Number of moles (n) = 0.05 mole
Rearranging the ideal gas law equation to solve for the final volume (V2):
V2 = (n * R * T2) / P
Using the appropriate values from Table 15.4, we can find the pressure for the given conditions. Let's assume it's 1 atm.
V2 = (0.05 * 0.0821 * 823) / 1 = 33.9385 L (rounded to 4 decimal places)
Therefore, the final volume of the air after compression will be approximately 33.9385 L.
(b) The change in internal energy of the air during compression can be calculated using the first law of thermodynamics, which states that ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Assuming this is an adiabatic compression process (no heat exchange with the surroundings), Q = 0.
ΔU = -W
ΔU = -PΔV
Since the pressure is constant (1 atm), we can calculate the change in volume (ΔV) as V2 - V1.
ΔV = V2 - V1
ΔV = 33.9385 L - 0.5 L = 33.4385 L
Now, we can calculate the change in internal energy:
ΔU = -PΔV
ΔU = -(1 atm)(33.4385 L)
ΔU = -33.4385 L-atm
Therefore, the change in internal energy of the air during compression is approximately -33.4385 L-atm.
(c) The work done by the piston on the gas while compressing it can be calculated using the equation W = -PΔV.
W = -(1 atm)(33.4385 L)
W = -33.4385 L-atm
The work done by the piston on the gas while compressing it is approximately -33.4385 L-atm.
(d) To find the highest temperature the gas will reach in cold weather, we can repeat the same calculations with the given conditions.
Initial temperature (T1) = 10 degrees Fahrenheit = -12.22 degrees Celsius = 260.78 K (rounded to 2 decimal places)
Using the same compression ratio and assuming the pressure remains constant at 1 atm, we can calculate the final temperature (T2):
V2 = (0.05 * 0.0821 * T2) / 1
Solving for T2:
T2 = (V2 * 1) / (0.05 * 0.0821)
Using the previous volume value of V2 = 33.9385 L:
T2 = (33.9385 * 1) / (0.05 * 0.0821)
T2 = 8283.52 K (rounded to 2 decimal places)
Now, converting the final temperature from Kelvin to Celsius:
T2 = 8283.52 K - 273.15 = 8010.37 degrees Celsius (rounded to 2 decimal places)
Therefore, the highest temperature the gas will reach in cold weather is approximately 8010.37 degrees Celsius.
(e) A diesel engine is hard to start in cold weather due to the low temperature affecting the compression and ignition processes. At low temperatures, the air-fuel mixture may not reach the required conditions for spontaneous ignition and combustion. This is a result of reduced air temperature leading to lower air density, which impacts the compression ratio and the rise in temperature during compression. Additionally, diesel fuel has a higher ignition temperature compared to gasoline.
Technological solutions to help start a diesel engine on a cold day include:
1. Glow plugs or grid heaters: These are electrical heating elements placed in the combustion chamber or intake manifold to preheat the air or fuel, ensuring a minimum temperature for easier ignition.
2. Block heaters: These are electric heaters that warm the engine block during cold weather, making it easier to start the engine.
3. Engine preheaters: These systems use external heating sources, such as engine coolant or electrical heating elements, to warm the engine before starting, ensuring higher temperatures for easier starting.
4. Fuel additives: Specific additives can improve the low-temperature flow characteristics of diesel fuel, making it easier to ignite and increasing the likelihood of successful starting.
It is important to note that these solutions may vary depending on the specific needs and requirements of different diesel engines and environmental conditions.