A sample of an ideal gas ( = 5 3 ) is heated at constant pressure. If 100J of heat is supplied to the gas , the work done by the gas is

Step-by-step solution

Applying the First Law of Thermodynamics for an ideal gas under constant pressure where heat Q = 100 J is supplied and the adiabatic index is = 5 3 . The first law states Q = U + W , with U representing the internal energy change and W the work done. For an ideal gas, U = n C_v T and W = n R T at constant pressure. Expressing U in terms of W gives U = C_v (W / R) . Using C_v = R / ( - 1) from the relation = C_p / C_v and C_p - C_v = R , then U = W / ( - 1) . Substituting into the first law: Q = W / ( - 1) + W = W [