Answer to Question #175396 in Molecular Physics | Thermodynamics for Bahaa

Question

An electrical resistance coil, wired to the surroundings, is placed inside a cylinder fitted with a frictionless piston and cont"]ning

an ideal gas' The walls of the cylinder and thepiston are adiabatic.

A current of 5 A is maintained through the resiitance, across which there is a voltage drop of 100 v. The piston is opposed by a constant

external force of 5000N. At what speed must the piston move outwards in order that there is no change in the tempeiature of the gas? Is the electrical energy transferred tothe gas as heat or work?

suppose now that the wans are diathermai and the resistance coil is wrapped round the outside of the cylinder. Regard the system the cylinder and the gas, excruding the heating coil. Is the energy transfer now heat of work?

Answer 1

Solution.

$I=5A;$

$U=100V;$

$F=5000N;$

$T=const;$

$v-?;$

$Q=A;$

$A=F\sdot l=F\sdot v\sdot t;$

$Q=I\sdot U\sdot t;$

$I\sdot U\sdot t=F\sdot v \sdot t \implies v=\dfrac{I\sdot U\sdot t}{F\sdot t}=\dfrac{I\sdot U}{F};$

$v=\dfrac{5A\sdot 100V}{5000N}=0.1m/s;$

The amount of heat received by the gas goes to work (the internal energy of the gas does not change).

Answer: $v=0.1m/s.$