In a particle-physics apparatus

PHYSICS · Multi-part · CBSE · Physics · Kinetic Theory · Kinetic Theory

Problem

In a particle-physics apparatus, a single proton is observed to have a translational kinetic energy of 0.040 electron-volts (eV). Useful information: • 1 eV=1.60×10−19 J1\,\text{eV}=1.60\times10^{-19}\,\text{J} • Boltzmann constant kB=1.38×10−23 J K−1k_{B}=1.38\times10^{-23}\,\text{J K}^{-1} • Avogadro’s number NA=6.022×1023 mol−1N_{A}=6.022\times10^{23}\,\text{mol}^{-1} (a) Convert the proton’s kinetic energy to joules. (b) Determine the temperature (in kelvins) that would give hydrogen gas molecules the same average kinetic energy as the proton described in part (a). (c) Suppose 1.00 L1.00\,\text{L} of ideal hydrogen gas at 1 atm and 298 K were suddenly given the total energy calculated in part (a). Estimate the new temperature of the gas, assuming no energy losses and that the amount of gas remains the same. (d) Evaluate whether the temperature rise found in part (c) would be experimentally detectable with common laboratory thermometers, and justify your reasoning.

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