In this problem you are to consider an adiabatic expansion of anideal diatomic gas, which means that the gas expands with noaddition or subtraction of heat.
This applet shows the adiabatic compression and expansion of anideal monatomic gas with \gamma=5/3. It will help you to see thequalitative behavior of adiabatic expansions, though your actualcalculations will use a slightly different gamma.
Assume that the gas is initially at pressure p_0, volume V_0, andtemperature T_0. In addition, assume that the temperature of thegas is such that you can neglect vibrational degrees of freedom.Thus, the ratio of heat capacities is \gamma=C_p/C_V=7/5.
Note that, unless explicitly stated, the variable gamma should notappear in your answers--if needed use the fact that \gamma=7/5 foran ideal diatomic gas.
A. Find an analytic expression for p(V), the pressure as a functionof volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the giveninitial values p_0, T_0, and V_0.
B. At the end of the adiabatic expansion, the gas fills a newvolume V_1, where V_1 > V_0. Find W, the work done by the gas onthe container during the expansion.
Express the work in terms of p_0, V_0, and V_1. Your answer shouldnot depend on temperature.
C. Find Delta U, the change of internal energy of the gas duringthe adiabatic expansion from volume V_0 to volume V_1.
Express the change of internal energy in terms of p_0, V_0, and/orV_1.
In this problem you are to consider an adiabatic expansion of anideal diatomic gas, which means that the gas expands with noaddition or subtraction of heat.
This applet shows the adiabatic compression and expansion of anideal monatomic gas with \gamma=5/3. It will help you to see thequalitative behavior of adiabatic expansions, though your actualcalculations will use a slightly different gamma.
Assume that the gas is initially at pressure p_0, volume V_0, andtemperature T_0. In addition, assume that the temperature of thegas is such that you can neglect vibrational degrees of freedom.Thus, the ratio of heat capacities is \gamma=C_p/C_V=7/5.
Note that, unless explicitly stated, the variable gamma should notappear in your answers--if needed use the fact that \gamma=7/5 foran ideal diatomic gas.
A. Find an analytic expression for p(V), the pressure as a functionof volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the giveninitial values p_0, T_0, and V_0.
B. At the end of the adiabatic expansion, the gas fills a newvolume V_1, where V_1 > V_0. Find W, the work done by the gas onthe container during the expansion.
Express the work in terms of p_0, V_0, and V_1. Your answer shouldnot depend on temperature.
C. Find Delta U, the change of internal energy of the gas duringthe adiabatic expansion from volume V_0 to volume V_1.
Express the change of internal energy in terms of p_0, V_0, and/orV_1.
