For monoatomic gas work done at constant pressure is W .For the same rise in temperature of the gas, the heat supplied at constant volume is

Step-by-step solution

At constant pressure, work done is: aligned & ₀^W d W=p _ V₁ ^ V₂ d V & W=p (V₂-V₁ ) aligned Using, p V=n R TW=n R (T₂-T₁ )=n R T Now, at constant volume, heat supplied is change in internal energy: aligned & d Q=n C_v T & ₀^Q d Q= _ T₁ ^ T₂ n ( R -1 ) d T & Q= n R (T₂-T₁ ) ( 5 3 -1 ) = 3 2 (n R T)= 3 W 2 & Q= n R T -1 , = 5 3 & Q= ( 3 2 ) n R T aligned