Question

In a thermally insulated cylinder with an internal cross section S = 500 cm2 and a height l =

= 50 cm, there is a resistor with resistance R = 120 Ω. The cylinder is otherwise filled with air

at a temperature T0 = 20 ◦C and pressure p0 = 101 kPa, and the same kind of air surrounds

the cylinder. A current I = 200 mA flows through the resistor. A base of the cylinder breaks

away when pushed with a force exceeding F = 500 N. After what time does that happen?

Answer 1

$F=(p-p_0)\cdot A$ ,

$m=\rho V=1.29\cdot500\cdot10^{-4}\cdot0.5=0.03225\ (kg)$

$M=28.96\cdot10^{-3}\ kg/mole$

$\nu=m/M=0.03225/0.02896=1.114\ (mole)$

$p_0V_0/T_0=pV_0/T\to p=p_0T/T_0$ or $F=(p_0T/T_0-p_0)A$

$Q=\Delta U\to Q=\frac{i}{2}\nu R(T-T_0)\to I^2rt=\frac{i}{2}\nu R(T-T_0)$

$T=\frac{2I^2rt}{i\nu R}+T_0$

$F=(p_0(\frac{2I^2rt}{i\nu R}+T_0)/T_0-p_0)A\to t=\frac{T_0i\nu RF}{2I^2rp_0A}=$

$=\frac{293\cdot5\cdot 1.114\cdot8.31\cdot500}{2\cdot 0.2^2\cdot 120\cdot101000\cdot 0.05}=140\ (s)$ . Answer