Question

When 'q' amount of heat is given to one mole of a monoatomic gas, it does q/2 amount of work on surroundings. Find the heat
capacity of the system in JK^-1 mol^-1
Take R= 8.314 J/K/mol].​

Answer 1

When q amount of heat is given to one mole of monoatomic gas. it does q/2 amount of work on surroundings.

To find : The molar heat capacity for the process.

solution : here heat given to system = q

work done on the surroundings, W = q/2

using first law of thermodynamics,

q = W + ∆U

⇒∆U = q - q/2 = q/2

for monoatomic gas,

∆U = 3/2 nR∆T

and q = nCp∆T

now, q/2 = 3/2 nR∆T

⇒nCp∆T/2 = 3/2 nR∆T

⇒Cp = 3R

Therefore the molar heat capacity for the process is 3R.

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