Two ideal gases, A and B, are at the same temperature, volume andpressure. Gas A

Question

Two ideal gases, A and B, are at the same temperature, volume andpressure. Gas A is reversibly expanded at constant temperature to avolume V. Gas B is allowed to expand into an evacuated chamberuntil it also has a total volume V, but without exchanging heatwith its surroundings. Which of the following most accuratelydescribes the two gases?

a. Gas A has a higher temperature andenthalpy than gas B.

b. Gas A has a highertemperature but a lower enthalpy than gas B.

c. Gas B has a highertemperature and enthalpy than gas A.

d. Gas A and B have equaltemperatures and enthalpies.

Explanation / Answer

Ideal gases: enthalpy and internal energy depend on onlytemperature Gas A is kept at constant temperature Gas B is allowed to expand but no heat is absorbed. dU = dQ + dW.In this case dQ = 0, dW = negative number, because gas is doingwork on the environment. Thus dU = negative number dU = Cv*dT . If dU is negative, so is dT. T must decrease forGas B. So Gas B is lower in temperature and also has a lower enthalpy (dH= Cp*dT) Note Cv and Cp are heat capacities at constant volume and pressure,respectively.

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