One kilogram of liquid water is placed in a pistoncylinder device, initially at P = 1 bar and T = 5°C. At these conditions, the density of water is 1000.4 g/L. The water is heated at constant pressure to T = 95°C, at which point the density is 962.3 g/L. The external pressure is also P = 1 bar.

A. Find the work and heat for this process. Use the temperature-dependent value of C_P given in Appendix D. Apply the relationship H = U + PV if conversion between H and U is necessary.

B. Find the heat for this process. This time, assume the density is constant at 1000 g/L, that C_P is constant at 4.19 J/g · K, that C_V ~ C_P, and that U ~ H for a liquid.

C. Compare your answers to parts A and B. The simplifying approximations in part B are often used for liquids (and solids); how well do they work here?