/* MJ-6: first-law signs, response identities, and printed answers. */
kill(all)$
print("first_law_numeric_residual =", subst([Q=500,W=120,dU=380],Q-W-dU))$
Ustate : C*T+Lambda*Vv^2/2$
print("state_temperature_derivative_residual =", ratsimp(diff(Ustate,T)-C))$
print("state_volume_derivative_residual =", ratsimp(diff(Ustate,Vv)-Lambda*Vv))$
V(T,p) := n*R*T/p$
alpha : ratsimp(diff(V(T,p),T)/V(T,p))$
kappa : ratsimp(-diff(V(T,p),p)/V(T,p))$
print("ideal_alpha_residual =", ratsimp(alpha-1/T))$
print("ideal_kappa_residual =", ratsimp(kappa-1/p))$
print("Mayer_response_residual =", ratsimp(T*V(T,p)*alpha^2/kappa-n*R))$
print("compression_volume_residual =", ratsimp(-(2/1000)*(5/10^10)*(2*10^7)-(-2/10^5)))$
print("thermal_volume_residual =", ratsimp((15/10000)*(3/10000)*80-36/10^6))$
print("response_heat_capacity_rounding_residual =", round(10*(300*1e-3*(1e-3)^2/1e-6))-3)$
print("rigid_stirring_residual =", subst([Q=-100,W=-500,dU=400],Q-W-dU))$