Temperature after air-motor expansion in compressed-air systems Considering a compressed-air system where an air motor expands the supplied compressed air to produce shaft work, how does the discharge air temperature compare to the original compressor intake temperature?

Introduction / Context:
Air motors convert the pressure energy of compressed air into mechanical work by expanding it. Gas expansion is accompanied by a temperature drop, the magnitude of which depends on the expansion path and efficiency.

Given Data / Assumptions:

• Air is supplied at a pressure higher than ambient.
• Expansion occurs in the motor to near-atmospheric exhaust pressure.
• Ambient compressor intake temperature is the reference for comparison.

Concept / Approach:
For an isentropic or near-isentropic expansion, T_out = T_in * (p_out/p_in)^((gamma-1)/gamma). Since p_out < p_in, the exponent is positive and the ratio is less than 1, leading to a lower discharge temperature. Even with non-idealities, the exhaust from an air motor is typically colder than ambient compressor intake temperature.

Step-by-Step Solution:
Recognise expansion process: pressure drop from supply to exhaust.Apply qualitative isentropic relation: temperature decreases with pressure in expansion.Conclude: discharge air temperature is less than the original intake temperature.

Verification / Alternative check:
Practical observations (frosting of outlets under heavy load) confirm significant cooling during expansion.

Why Other Options Are Wrong:

• “More/greater” contradict expansion thermodynamics.
• “Same under all conditions” ignores process dependence.
• “Undefined” is incorrect; temperature change is fundamental to gas expansion.

Common Pitfalls:
Confusing compressor discharge temperature with intake temperature; aftercooling and piping losses do not negate the cooling effect of downstream expansion in the motor.

Final Answer:
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