3.7.3 Experimental principles
According to thermodynamic,the specific heat(capacity)ratio of a gas is defined as the ratio of the specific heat(capacity)at constant pressure CP to its specific heat(capacity)at a constant volume CV,which can be expressed as:
Here,the symbol γ is the specific heat ratio of the gas(or the adiabatic index).The specific heat ratio is important in thermodynamical reversible processes,especially involving ideal gases.Many methods,including the vibration method,resonance method,sonic velocity method,and adiabatic expansion or compression method,are utilized to determine the specific heat ratio of a gas.Among them,the adiabatic expansion method is a simple approach to roughly measure the specific heat ratio of air,which is helpful for students to observe the thermodynamic phenomenon and understand the thermodynamic state.Here,the adiabatic process refers to no heat transfer between the study system and its surroundings.
In the air cylinder system,the atmospheric pressure and temperature are assumed to be p0 and T0,respectively.First of all,open the inlet valve C1 and close the outlet valve C2.The air is slowly pumped into the bottle by the inflating ball and then close the inlet valve C1.Now,the air in the bottle is compressed with both pressure and temperature increasing.Then,the air temperature in the bottle will slowly decrease to atmospheric temperature T0 due to the heat exchange through the wall of the bottle.Therefore,the air in the bottle is in stateⅠ(p1,V1,T0)if waiting an enough long time,as shown in Figure 3.7.3(a).The process above is a constant volume heat process.
Secondly,open the outlet valve C2 to quickly release the air from the bottle to the outside.When the pressure drops to P0,then immediately close C2.The air releasing process is too fast to exchange the heat with the surrounding air.Therefore,it can be considered as an adiabatic expansion process.Now,the state of the air in the bottle is transformed into stateⅡ(p0,V2,T1),as displayed in Figure 3.7.3(b).
Thirdly,the air in the bottle will slowly absorb heat from outside because the air temperature T1 in the bottle is lower than that of the surrounding.The heat exchange process will stop until the temperature in the bottle reaches T0.Now,stateⅢ(p2,V2,T0)can be achieved,as shown in Figure 3.7.3.(c).
Figure 3.7.3 Schematic diagram of three gas states(https://www.daowen.com)
StateⅠto stateⅡis an adiabatic process,therefore,it can be expressed as:
For the same system,the temperature of stateⅠand stateⅢis the same.Thus,the process from stateⅠto stateⅢis an isothermal process,so we have:
According to Equation(3.7.2)and Equation(3.7.3),and eliminating V1 and V2,then γ can be expressed as:
Clearly,the specific heat ratio of air can be calculated by measuring p0,p1 and p2.
