A high-performance pneumatic shock absorber contains a chamber filled with nitrogen gas. During a sudden compression, such as when a vehicle hits a bump, the gas behaves adiabatically, affecting the suspension stiffness.
The first law of thermodynamics can be written as:
Q=ΔU+W Q = \Delta U + W Q=ΔU+WState what ΔU\Delta UΔU represents in this equation.
During a sudden bump, the nitrogen chamber is compressed adiabatically. The work done on the nitrogen gas during this compression is 180 J180\text{ J}180 J.
Which row in the table below correctly represents the values of WWW, QQQ, and ΔU\Delta UΔU for this compression?
| W / JW \text{ / J}W / J | Q / JQ \text{ / J}Q / J | ΔU / J\Delta U \text{ / J}ΔU / J | |
|---|---|---|---|
| Row A | 180180180 | 000 | −180-180−180 |
| Row B | −180-180−180 | 000 | 180180180 |
| Row C | −180-180−180 | −180-180−180 | 000 |
| Row D | 180180180 | 180180180 | 000 |
The initial conditions for the nitrogen gas in the chamber are:
During rapid operation, the chamber is compressed adiabatically to a volume of 1.50×10−4 m31.50 \times 10^{-4}\text{ m}^31.50×10−4 m3.
Calculate the pressure and temperature of the nitrogen immediately after the compression. Take γ\gammaγ for nitrogen as 1.401.401.40.
To produce the adiabatic change, the shock absorber is compressed very rapidly. An engineer suggests that by compressing the chamber slowly to the same final volume of 1.50×10−4 m31.50 \times 10^{-4}\text{ m}^31.50×10−4 m3, the work done to compress the gas will be greater than 180 J180\text{ J}180 J.
Deduce, without calculation, whether the engineer is correct.
