Write down the thermodynamic equations of state for the pressure and entropy which follow from the Helmholtz free energy F. Hence express the heat capacity at constant volume in terms of F. [You may use the definition: dF = −SdT – PdV.]

At steady state, a thermodynamic cycle operating between hot and cold reservoirs at 1000 K and 500 K, respectively, receives energy by heat transfer from the hot reservoir at a rate of 1500 kW, discharges energy by heat transfer to the cold reservoir, and develops power at a rate of (a) 1000 kW, (b) 750 kW, (c) 0 kW. For each case, apply Eq. 5.13 on a time- rate basis to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.

For a p, v, T system formed by a mole, it has been empirically obtained that the internal energy per unit mass can be written in the form: u = apv+b, where a, b are constants. Find the equation for the adiabat in this system.

This is a thermodynamics question! Please consider all equations for thermo. Please show all steps and ensure the answer is in the correct units!   NO TUTOR HAS GOTTEN THIS RIGHT YET :(