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The pressure and temperature at the start of compression of diesel cycle is 1 bar and 15°C. The pressure at the end of expansion is 4bar, the maximum temperature when the compression ratio is 15 and the specific heat at constant pressure is 1.008 kJ/kgK is ____°C
Correct answer is '2017'. Can you explain this answer?
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°C respectively. The compression ratio is 16 and the specific heat ratio is 1.4. Find the pressure and temperature at the end of compression.
To solve this problem, we can use the ideal gas law and the equation for the specific heat ratio.
1. Convert the temperature from Celsius to Kelvin:
T1 = 15°C + 273.15 = 288.15 K
2. Use the compression ratio to find the end volume of compression:
V2/V1 = (compression ratio)^(-1)
V2/V1 = 16^(-1) = 0.0625
3. Use the ideal gas law to find the pressure at the end of compression:
P1V1/T1 = P2V2/T2
P2 = P1*(V1/V2)*(T2/T1)
P2 = 1 bar * 0.0625 * (T2/288.15)
4. Use the equation for the specific heat ratio to find the temperature at the end of compression:
T2/T1 = (V1/V2)^(gamma - 1)
T2 = T1 * (V1/V2)^(gamma - 1)
T2 = 288.15 K * (0.0625)^(1.4 - 1)
Calculating the values:
P2 = 1 bar * 0.0625 * (T2/288.15)
T2 = 288.15 K * (0.0625)^(1.4 - 1)
P2 = 0.0625 bar * (T2/288.15)
T2 = 288.15 K * 0.0625^(0.4)
P2 ≈ 0.00390625 bar ≈ 0.004 bar (rounded to three decimal places)
T2 ≈ 288.15 K * 0.325 ≈ 93.748 K ≈ 93.75 K (rounded to two decimal places)
Therefore, the pressure at the end of compression is approximately 0.004 bar and the temperature at the end of compression is approximately 93.75 K.
To solve this problem, we can use the ideal gas law and the equation for the specific heat ratio.
1. Convert the temperature from Celsius to Kelvin:
T1 = 15°C + 273.15 = 288.15 K
2. Use the compression ratio to find the end volume of compression:
V2/V1 = (compression ratio)^(-1)
V2/V1 = 16^(-1) = 0.0625
3. Use the ideal gas law to find the pressure at the end of compression:
P1V1/T1 = P2V2/T2
P2 = P1*(V1/V2)*(T2/T1)
P2 = 1 bar * 0.0625 * (T2/288.15)
4. Use the equation for the specific heat ratio to find the temperature at the end of compression:
T2/T1 = (V1/V2)^(gamma - 1)
T2 = T1 * (V1/V2)^(gamma - 1)
T2 = 288.15 K * (0.0625)^(1.4 - 1)
Calculating the values:
P2 = 1 bar * 0.0625 * (T2/288.15)
T2 = 288.15 K * (0.0625)^(1.4 - 1)
P2 = 0.0625 bar * (T2/288.15)
T2 = 288.15 K * 0.0625^(0.4)
P2 ≈ 0.00390625 bar ≈ 0.004 bar (rounded to three decimal places)
T2 ≈ 288.15 K * 0.325 ≈ 93.748 K ≈ 93.75 K (rounded to two decimal places)
Therefore, the pressure at the end of compression is approximately 0.004 bar and the temperature at the end of compression is approximately 93.75 K.
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The pressure and temperature at the start of compression of diesel cycle is 1 bar and 15°C. The pressure at the end of expansion is 4bar, the maximum temperature when the compression ratio is 15 and the specific heat at constant pressure is 1.008 kJ/kgK is ____°CCorrect answer is '2017'. Can you explain this answer?
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