Problem 10: A mass m of a material is heated reversibly from temperature T1 to T2 at a constant pressure of P. In this problem, we are going to determine an expression for the change in entropy, ΔS. Assume we can heat the given material infinitesimally slowly so that the process is reversible. Therefore, heat in any infinitesimal step is given by the following: dQ = mcpdT, where cp is the specific heat. In general, the heat capacity of a material can be temperature-dependent. A general temperature-dependent empirical form for the specific heat for ideal gases and incompressible liquids such as water is as follows: cp(T) = A + BT + CT 2 + DT -2, where A, B, C, and D are substance-dependent constants that can be determined empirically. Part (a) Determine the change in entropy, in calories per kelvin, for a sample of incompressible fluid with mass m = 2.3 kg and changing temperature from T1 = 18.8°C to T2 = (18.8+10)°C. The constant A = 993 cal/(kg K), B = 993 • 10-2 cal/(kg K2), C = D = 0.
Problem 10: A mass m of a material is heated reversibly from temperature T1 to T2 at a constant pressure of P. In this problem, we are going to determine an expression for the change in entropy, ΔS. Assume we can heat the given material infinitesimally slowly so that the process is reversible. Therefore, heat in any infinitesimal step is given by the following:
dQ = mcpdT,
where cp is the specific heat. In general, the heat capacity of a material can be temperature-dependent. A general temperature-dependent empirical form for the specific heat for ideal gases and incompressible liquids such as water is as follows:
cp(T) = A + BT + CT 2 + DT -2,
where A, B, C, and D are substance-dependent constants that can be determined empirically.
Part (a) Determine the change in entropy, in calories per kelvin, for a sample of incompressible fluid with mass m = 2.3 kg and changing temperature from T1 = 18.8°C to T2 = (18.8+10)°C. The constant A = 993 cal/(kg K), B = 993 • 10-2 cal/(kg K2), C = D = 0.
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