Define the internal energy of an ideal gas.
Use the formulae below to show that the average kinetic energy of a particle of an ideal gas is directly proportional to the absolute temperature of the gas.
pV=13Nmc2‾andpV=NkT pV = \frac{1}{3}N m \overline{c^2} \quad \text{and} \quad pV = NkT pV=31Nmc2andpV=NkTThe velocities of four gas particles at 290 K290\text{ K}290 K are given below in m s−1\text{m s}^{-1}m s−1:
290,360,410,520 290, \quad 360, \quad 410, \quad 520 290,360,410,520Show that the root-mean-square (r.m.s.) speed of the sample is approximately 400 m s−1400\text{ m s}^{-1}400 m s−1.
The velocities of four gas particles at 290 K290\text{ K}290 K are given below in m s−1\text{m s}^{-1}m s−1:
290,360,410,520 290, \quad 360, \quad 410, \quad 520 290,360,410,520Calculate the molar mass of the gas assuming an absolute temperature of 290 K290\text{ K}290 K and an r.m.s. speed of 400 m s−1400\text{ m s}^{-1}400 m s−1.
A sealed gas-filled ionization detector is manufactured by filling it with a noble gas at 290 K290\text{ K}290 K and low pressure.
When the detector is installed in an industrial monitoring system, it is exposed to constant thermal radiation and reaches a stable operating temperature of 980 K980\text{ K}980 K. At this temperature, the pressure inside the sealed detector is 220 kPa220\text{ kPa}220 kPa.
Explain, in terms of energy transfers, why the operating temperature of the detector remains constant at 980 K980\text{ K}980 K rather than continuing to rise. You are not expected to refer to the electrical properties of the detector.
A sealed gas-filled ionization detector is manufactured by filling it with a noble gas at 290 K290\text{ K}290 K and low pressure.
When the detector is installed in an industrial monitoring system, it is exposed to constant thermal radiation and reaches a stable operating temperature of 980 K980\text{ K}980 K. At this temperature, the pressure inside the sealed detector is 220 kPa220\text{ kPa}220 kPa.
Calculate the pressure of the gas within the detector during manufacture (at 290 K290\text{ K}290 K).
