A miniature pneumatic actuator on a high-precision robotic probe is used to position samples in a vacuum chamber. The actuator contains a small quantity of nitrogen gas.
When the actuator's control rod is driven rapidly inwards, it compresses the nitrogen gas inside, causing its temperature to rise. Explain how this increase in temperature affects the motion of the nitrogen molecules and the pressure they exert on the internal surfaces of the actuator chamber.
In a test of the actuator, the work done on the nitrogen gas during a rapid compression stroke transfers 0.0234 J0.0234\text{ J}0.0234 J of energy to the gas. The mass of nitrogen gas in the chamber is 5.00×10−8 kg5.00 \times 10^{-8}\text{ kg}5.00×10−8 kg. The specific heat capacity of nitrogen gas is 1040 J/kg ∘C1040\text{ J/kg }^{\circ}\text{C}1040 J/kg ∘C.
Calculate the temperature change of the nitrogen gas.