A compressor brings nitrogen from 100 kPa, 290 K to 2000 kPa. The process has a specific work input of 450 kJ / kg and the exit temperature is 450 K. Find the specific heat transfer using constant specific heats

Given Information:

Gas = Nitrogen

Inlet temperature = T₁ = 290 K

Exit temperature = T₂ = 450 K

Inlet Pressure = P₁ = 100 kPa

Exit Pressure = P₂ = 2000 kPa

Work input = W = -450 kJ/kg

Required Information:

specific heat transfer = Q = ?

specific heat transfer = - 282.64 KJ/kg

Explanation:

The specific heat transfer can be found using the equation

Q - W = ΔU

Q = ΔU + W   eq. 1

Where W is the work input and ΔU is the change in internal energy.

The change in specific internal energy is given by

ΔU = h₂ - h₁ = Cp(T₂ - T₁)

Where Cp is the specific heat capacity.

The specific heat capacity is the amount of heat required to increase the temperature of one gram of a substance by one degree K.

The Cp of Nitrogen gas is equal to 1.046 KJ/kg.K

Therefore, equation 1 becomes

Q = ΔU + W

Q = Cp(T₂ - T₁) + W

Q = 1.046(450 - 290) + (-450)

Q = 1.046(160) - 450

Q = 167.36 - 450

Q = - 282.64 KJ/kg

The negative sign indicates that the heat energy was transferred from the system (leaving the system) rather than transferred to the system (entering the system).

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