An ideal monatomic gas undergoes a cyclic process A B C D A as described on a Pressure-Volume ( P-V ) diagram. The cycle forms a rectangle with vertices at A(V₀, P₀) , B(V₀, 2P₀) , C(2V₀, 2P₀) , and D(2V₀, P₀) . The heat supplied to the gas during the isobaric expansion segment is:

Step-by-step solution

The isobaric expansion segment is the process B C , where the pressure is constant at 2P₀ and the volume increases from V₀ to 2V₀ . The work done during this process is: W = P V = 2P₀(2V₀ - V₀) = 2P₀V₀ The change in internal energy for a monatomic ideal gas is: U = 3 2 nR T = 3 2 P V U = 3 2 (2P₀)(V₀) = 3P₀V₀ According to the First Law of Thermodynamics, the heat supplied is: Q = W + U Q = 2P₀V₀ + 3P₀V₀ = 5P₀V₀ Alternatively, using molar heat capacity at constant pressure for a monatomic gas ( C_p = 5 2 R ): Q = nC