# Temperature of ideal gas in a cylinder

12 An ideal gas is contained in an insulating cylinder fitted with a piston, as shown.

The piston is suddenly moved inwards so that the volume of the gas is reduced. What happens to the temperature of the gas?

A It increases because the gas molecules bounce off the piston at higher speeds.
B It increases because the gas molecules collide with each other more often.
C It stays constant because $$\mathrm{pressure \times volume}$$ is constant for an ideal gas.
D It stays constant because the cylinder is an insulator.

Why is option A and C wrong or correct?

A: is plausible as if the piston is suddenly moved inwards, the gas molecules bounce off the piston at higher speeds. Since temperature is proportional to rms speed, temperature increases.

Or, based on 1st law of thermodynamics, the piston suddenly moved in. So means $$Q = 0$$ because there is no time for the heat transfer. Since compression, $$W$$ is +ve, so $$U$$ is +ve. That implies $$T$$ increases.

C: as $$P$$ increases, $$V$$ decreases.