Answer Happy

Say an ideal gas (P V = N k T) is kept at constant temperature
while heat is added because its volume is allowed to vary from V to
2 V (that is its volume doubles).
Using the first law of thermodynamics, how much heat was added
(to double the volume of a gas while maintaining constant
temperature and number of molecules N; k is Boltzmann's
constant)?
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Hint:
The first law of thermodynamics (for an infinitesimal change in a
gas) is
dU = dQ - P dV
where internal energy U of an ideal gas is a function of
temperature T only; Q is the heat added to the system; and - P dV
is the work done on the system by pressure P.
Write your answer as an equation in terms of the number
of molecules N and the temperature T in kelvin (both maintained as
constants in this problem).