Question

# The molar heat capacity in a process of diatomic gas if it does a work of $$\dfrac{Q}{4}$$ when a heat of Q is supplied to it is

A
25R
B
54R
C
103R
D
64R

Solution

## The correct option is B $$\dfrac{10}{3}$$RFirst law of Thermodynamics we have :-$$Q=w+ΔU$$   (1)where,Q = Heat supplied to the gasw = Work done by the gasΔU = Change in the internal energy of the gasGiven :-$$w=Q/4$$     (2)From (1) & (2) we have :-⟹$$ΔU=3Q/4$$      (3)Now,$$ΔU=\dfrac{nRΔT}{γ−1}$$  (4)where,n = No. of moles of gasΔT = Change in temperatureR = Universal Gas Constantγ = Specific heat ratioFor a diatomic gas :-$$γ=7/5$$          ( 5)Using (3), (4) & (5) we get :-⟹$$nΔT=\dfrac{3Q}{10R}$$        (6)Also note that :-$$Q=nCΔT$$      (7)where,C = Molar specific heat for the processSo now replace nΔT in (7) by (6) :-⟹$$\dfrac{3QC}{10R}=Q$$⟹$$C=\dfrac{10R}{3}$$Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More