Question

Find kinetic energy of 1 litre of an ideal gas at S.T.P.

Hint:

The formula \( K.E. = \frac{3}{2} PV \) is a direct and quick way to find the total kinetic energy if you know the pressure and volume, avoiding the need to calculate the number of moles.

Answer 1

The total translational kinetic energy of an ideal gas is given by the formula: \[ K.E. = \frac{3}{2} PV \] At Standard Temperature and Pressure (S.T.P.):
Pressure, \( P = 1 \, \text{atm} \approx 1.013 \times 10^5 \, \text{Pa} \)
Volume, \( V = 1 \, \text{litre} = 10^{-3} \, m^3 \)
Substituting the values: \[ K.E. = \frac{3}{2} \times (1.013 \times 10^5 \, \text{Pa}) \times (10^{-3} \, m^3) \] \[ K.E. = 1.5 \times 1.013 \times 10^2 \, J \] \[ K.E. \approx 152 \, J \] The kinetic energy of 1 litre of an ideal gas at S.T.P. is approximately 152 Joules.