Question

A vessel containing one mole of a monatomic ideal gas (molecular weight = $20gmo{l}^{-1}$ is moving on a floor at aspeed of 50 $m.s^{-1}.$ The vessel is stopped suddenly. Assuiming that the mechnical energy lost has gone into the internal energy of the gas, find the rise in its temperature.

Answer 1

N = 1 mole,

W = 20 g/mole, V= 50 m/s

K.E. of the vesel = internal energy of the gas

K.E = $\frac{1}{2}m{V}^2$

=$\frac{1}{2}\times 20\times {10}^{-3}\times 50\times 50$

= 25 J.

So, 25 = $\frac{3}{2}nR\left(\Delta T\right)$

$\Rightarrow 25=1\times \frac{3}{2}\times 8.31\times \Delta T$

$\Rightarrow \Delta T=\frac{50}{(3\times 8.3)}$ = 2 K