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Hi everyone,
I have just come across a possibly faulty question perhaps related to
John Denker's question on heat.....
(a) A car tyre has a fixed internal volume of 0.0120 m3. On a day when
the temperature is 25 degC the pressure in the tyre has to be
increased from 2.62 X 10^5 Pa to 3.23 X 10^5 Pa. Assuming the air is
an ideal gas, calculate the amount of air which has to be supplied at
constant temperature.
(b) Apply the first law of thermodynamics to the pressure increase in
(a) in order to calculate the amount of work which has to be done to
increase the pressure.
The question has possibly at least three problems:
1. By supplying more air into the tyre, it has changed the system. The
system gain internal energy from the increase in molecules with
kinetic energy. (First law of thermodynamics does not quite apply
here, by work done or heat transfer.) The system has more molecules
than before. The system has changed.
2. The question does not specify whether the tyre is well insulated,
and heat transfer may still take place. The temperature inside the
tyre could have changed.
3. The tyre should be inflated to a larger volume. The question is
somewhat contrived that it can be misleading to the students.
Do you define work done on fixed-volume system when the pressure is
increased by pumping more air molecules? The work done can also be
considered by compressing the initial volume of air, since the
effective volume of the initial air is smaller? There seems no mention
of this kind of work in Mallinckrodt’s “All about work”. (Just a
cursory read.)
Best regards,
Alphonsus
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