A mass of 8kg gas expands within a flexible container so that p-vrelationship is of the form pv1.2=c. The initial pressure is 1000kPa and initialvolume is 1m3. The final pressure is 5kPa. If specific internal energy of gasdecreases by 40 kJ/kg, find the heat transfer.
Question
A mass of 8kg gas expands within a flexible container so that p-vrelationship is of the form pv1.2=c. The initial pressure is 1000kPa and initialvolume is 1m3. The final pressure is 5kPa. If specific internal energy of gasdecreases by 40 kJ/kg, find the heat transfer.
Solution
To solve this problem, we need to use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
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First, calculate the work done by the system. The work done (W) in a polytropic process can be calculated using the formula:
W = (P2V2 - P1V1) / (1-n)
where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the polytropic index. In this case, P1 = 1000 kPa, V1 = 1 m^3, P2 = 5 kPa, and n = 1.2.
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Next, calculate the change in internal energy (ΔU). The change in internal energy can be calculated using the formula:
ΔU = m * Δu
where m is the mass of the gas and Δu is the change in specific internal energy. In this case, m = 8 kg and Δu = -40 kJ/kg.
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Finally, calculate the heat transfer (Q) using the first law of thermodynamics. The heat transfer can be calculated using the formula:
Q = ΔU + W
Substitute the values of ΔU and W from steps 1 and 2 into this formula to find the heat transfer.
Remember that the work done by the system is negative if the volume is increasing (as it is in this case), and the change in internal energy is negative if the internal energy is decreasing (as it is in this case).
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