Question

A monatomic gas is cooled by 50

Answer 1

The main principle in this question is the First law of Thermodynamics
By 1st Law, dQ=dW+dU (using d for delta,nevertheless)
dW=0 as volume is constant
So, dQ=dU

Now, for monoatomic gases, Molar specific heat at constant volume is given by 3/2.R,where R=gas const.
as dU=nCdT, the values can be substituted to get the only unknown n, which is the no.of moles.

(Monoatomic is explicitly mentioned so that the Cv of the gas can be found out based on equipartition of energy)

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