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whatisreality
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Homework Statement
The volume of 30.0 moles of a monoatomic ideal gas is reduced at a uniform rate from 0.616m3 to 0.308m3 in 2h. Its temperature is increased at a uniform rate from 27.0◦C to 450◦C. The gas passes through thermodynamic equilibrium states throughout.
(a) Write down explicitly how the temperature and the volume of the gas depend on time (in hours). Then find the dependence of T on V explicitly.
(b) Calculate the cumulative work done by the gas.
(c) Calculate the cumulative energy absorbed by the gas as heat.
Homework Equations
The Attempt at a Solution
For part a), pretty sure dV/dt = 0.154 and dT/dt = 211.5. If that's the case then making dt the subject and equation both gives
0.154 dT = 211.5 dV
b) I can't add together the work done in the volume change, then add work to change temperature, because of the path dependence of work. This is definitely an integral! Which I am really struggling to form...