Question

One kilogram of water (v1 = 1,003 cm3 kg-1) in a piston/cylinder device at 25°C and 1 bar is compressed in a mechanically reversible, isothermal process to 1,500 bar. Determine q, w, ∆u, ∆h, and ∆s given that β = 250 x 10-6 K -1 and κ = 45 x 10-6 bar-1.

Answer 1

The work done by the gas during an isothermal process can be calculated using the ideal gas law formula W = nRT ln(P2/P1), where 'n' is the number of moles, 'R' is the universal gas constant, 'T' is the temperature, and 'P1' and 'P2' are the initial and final pressures.

Step-by-step explanation:

The work done by the gas in a thermodynamic process can be calculated using the ideal gas law, often in the context of an isothermal expansion or compression. For a process where the temperature remains constant, the work done by the gas as it changes from an initial pressure P1 to a final pressure P2 can be found using the formula:

W = nRT ln(P2/P1)

Where n is the number of moles of the gas, R is the universal gas constant, T is the absolute temperature, and P1 and P2 are the initial and final pressures, respectively. For an isothermal expansion against a constant pressure, the work done is equal to the product of pressure and the change in volume, i.e., W = P(V2 - V1), where V2 and V1 are the final and initial volumes respectively. In the case of an adiabatic process, no heat is exchanged with the surroundings and the work done on or by the gas results in a change in the internal energy of the gas.