A compressor is used to compress air from an initial state of 100 kPa and 300 K to a final state of 800 kPa. Determine the work done on the air and the final temperature if the compression process is isentropic.
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To calculate the work done on the air during the isentropic compression process, we can use the equation:
W = C_p * (T2 - T1)
Where:
W = work done on the air
C_p = specific heat capacity of the air (assumed constant)
T2 = final temperature = T1 * (P2 / P1)^((gamma - 1) / gamma)
Given:
P1 = 100 kPa
T1 = 300 K
P2 = 800 kPa
gamma = the specific heat capacity ratio (assumed constant for air) = 1.4
First, let's calculate the final temperature (T2) using the formula above:
T2 = T1 * (P2 / P1)^((gamma - 1) / gamma)
= 300 * (800 / 100)^((1.4 - 1) / 1.4)
≈ 522.3 K
Next, we can substitute T2 and T1 into the work equation to calculate the work done on the air:
W = C_p * (T2 - T1)
= C_p * (522.3 - 300)
However, we do not have the value of specific heat capacity (C_p) given. If you have this information, please provide it so that we can calculate the work done on the air.
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