Thermodynamics

180 | ThermodynamicsAIRm = 1 kg300 301 KAIR(high pressure)←ThermometerWATERAIRm = 1 kg1000 1001 K0.718 kJ 0.855 kJFIGURE 4–21The specific heat of a substancechanges with temperature.INTERACTIVETUTORIALSEE TUTORIAL CH. 4, SEC. 4 ON THE DVD.EvacuatedFIGURE 4–22Schematic of the experimentalapparatus used by Joule.←volume. Likewise, c p can be defined as the change in the enthalpy of a substanceper unit change in temperature at constant pressure. In other words,c v is a measure of the variation of internal energy of a substance with temperature,and c p is a measure of the variation of enthalpy of a substance withtemperature.Both the internal energy and enthalpy of a substance can be changedby the transfer of energy in any form, with heat being only one of them.Therefore, the term specific energy is probably more appropriate than theterm specific heat, which implies that energy is transferred (and stored) inthe form of heat.A common unit for specific heats is kJ/kg · °C or kJ/kg · K. Notice thatthese two units are identical since T(°C) T(K), and 1°C change intemperature is equivalent to a change of 1 K. The specific heats are sometimesgiven on a molar basis. They are then denoted by c – v and c– p and havethe unit kJ/kmol · °C or kJ/kmol · K.4–4 INTERNAL ENERGY, ENTHALPY,AND SPECIFIC HEATS OF IDEAL GASESWe defined an ideal gas as a gas whose temperature, pressure, and specificvolume are related byPv RTIt has been demonstrated mathematically (Chap. 12) and experimentally(Joule, 1843) that for an ideal gas the internal energy is a function of thetemperature only. That is,u u 1T2(4–21)In his classical experiment, Joule submerged two tanks connected with apipe and a valve in a water bath, as shown in Fig. 4–22. Initially, one tankcontained air at a high pressure and the other tank was evacuated. Whenthermal equilibrium was attained, he opened the valve to let air pass fromone tank to the other until the pressures equalized. Joule observed nochange in the temperature of the water bath and assumed that no heat wastransferred to or from the air. Since there was also no work done, he concludedthat the internal energy of the air did not change even though thevolume and the pressure changed. Therefore, he reasoned, the internalenergy is a function of temperature only and not a function of pressure orspecific volume. (Joule later showed that for gases that deviate significantlyfrom ideal-gas behavior, the internal energy is not a function of temperaturealone.)Using the definition of enthalpy and the equation of state of an ideal gas,we haveh u Pvfh u RTPv RTSince R is constant and u u(T), it follows that the enthalpy of an ideal gasis also a function of temperature only:h h 1T2(4–22)