Question

Consider that an ideal gas (n moles) is expanding in a process given by P = f (V), which passes through a point (P₀, V₀). Show that the gas is absorbing heat at (P₀,V₀) is the slope of the curve P = f (V) is larger than the slope of the adiabat passing through (P₀, V₀).

Answer 1

From question – 

Slope of P = f (V), curve at (V₀, P₀) 

= f(V₀) 

Now heat absorbed in the process P = f(V)

\(=k(-\gamma)V_{0}^{-1-\gamma}\)=\(=-\frac{\gamma P_0}{V_0}\)

Now heat absorbed in the process P = f(V) 

dQ = dV + dW 

dQ = nC_VdT + PdV       …(I) 

PV = nRT or T = P\(\frac{V}{nR}\)

Since P=f(V) 

T = (1/nR) PV = (1/nR)V f(V) 

dT = (1/nR)[f(V) + V f'(V)] dV   …(II) From (I)