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Calculate max Temp reached, change in internal energy, heat transfer during process ?
Anonymous
Mar 6
Calculate max Temp reached, change in internal energy, heat transfer during process ?
Constant Vol=0.2m^3 mixture of fuel and air at 1.2 bars and 60°c compressed pressure to 12bars with Temp 270°c with constant volume and it's pressure becomes twice the pressure at the end of compression. Calculate max Temp reached, change in internal energy, heat transfer during process ?
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ChatGPT
Mar 6
Given:
Initial volume (V1) = 0.2 m^3
Initial pressure (P1) = 1.2 bars
Initial temperature (T1) = 270°C = 543 K
Final pressure (P2) = 2 * P1 = 2 * 1.2 = 2.4 bars
Since the process is constant volume, we can use the ideal gas law to find the final temperature (T2) reached:
P1/T1 = P2/T2
T2 = (P2/P1) * T1
T2 = (2.4/1.2) * 543
T2 = 1086 K
Now, we can calculate the change in internal energy (ΔU) using the first law of thermodynamics:
ΔU = Q - W
Since the process is constant volume, no work is done (W = 0). Therefore, the change in internal energy is equal to the heat added (Q):
ΔU = Q
Q = n*Cv*(T2 - T1)
Where:
n = number of moles of gas
Cv = molar specific heat at constant volume
To find the number of moles of gas, we can use the ideal gas law:
PV = nRT
n = PV / RT
n = (1.2 * 0.2) / (8.31 * 543)
n = 0.000443 moles
Now, we can calculate the change in internal energy:
ΔU = 0.000443 * Cv * (1086 - 543)
Assuming Cv = 20.8 J/mol*K for air at constant volume:
ΔU = 0.000443 * 20.8 * (1086 - 543)
ΔU = 0.000443 * 20.8 * 543
ΔU = 4.67 kJ
Therefore, the maximum temperature reached is 1086 K and the change in internal energy is 4.67 kJ.
Initial volume (V1) = 0.2 m^3
Initial pressure (P1) = 1.2 bars
Initial temperature (T1) = 270°C = 543 K
Final pressure (P2) = 2 * P1 = 2 * 1.2 = 2.4 bars
Since the process is constant volume, we can use the ideal gas law to find the final temperature (T2) reached:
P1/T1 = P2/T2
T2 = (P2/P1) * T1
T2 = (2.4/1.2) * 543
T2 = 1086 K
Now, we can calculate the change in internal energy (ΔU) using the first law of thermodynamics:
ΔU = Q - W
Since the process is constant volume, no work is done (W = 0). Therefore, the change in internal energy is equal to the heat added (Q):
ΔU = Q
Q = n*Cv*(T2 - T1)
Where:
n = number of moles of gas
Cv = molar specific heat at constant volume
To find the number of moles of gas, we can use the ideal gas law:
PV = nRT
n = PV / RT
n = (1.2 * 0.2) / (8.31 * 543)
n = 0.000443 moles
Now, we can calculate the change in internal energy:
ΔU = 0.000443 * Cv * (1086 - 543)
Assuming Cv = 20.8 J/mol*K for air at constant volume:
ΔU = 0.000443 * 20.8 * (1086 - 543)
ΔU = 0.000443 * 20.8 * 543
ΔU = 4.67 kJ
Therefore, the maximum temperature reached is 1086 K and the change in internal energy is 4.67 kJ.
0
Kabugho Gorret
Mar 6
813°c, 143.kj
0
