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Reason being vaguely adiabatic process is more rapid - process is done so fast that no energy is allowed to enter or exit the system. So P-v variations will be high

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Why an adiabatic curve steeper than an iosthermal?

In isothermal the temperature is constant whereas in adiabatic the temperature falls or rises rapidly.Consider the case for expansion where in adiabatic the temperature drops. If you consider PV/T=constant then for same pressure we can show that as temp decreases the volume also decreases. During expansion for isothermal the temp does not change so volume is higher than adiabatic. Example: Isothermal P=8 Pa, V=x , T=2K Adiabatic P=8 Pa, V=y, T=1K (as it drops) Using PV/T=constant we can find that y is less than x.


Why adiabatic is steeper than isotherm?

An adiabatic curve is steeper than an isothermal curve because it represents a process where no heat is exchanged with the surroundings, leading to a more significant change in pressure and temperature for a given volume change. In contrast, an isothermal process occurs at constant temperature, so the system can absorb heat to maintain that temperature, resulting in a more gradual slope on a pressure-volume diagram. Essentially, the lack of heat exchange in an adiabatic process restricts the system's ability to adjust temperature, causing a steeper relationship between pressure and volume changes.


What is ratio of adiabatic elasticity isothermal elasticity?

The ratio of adiabatic elasticity to isothermal elasticity is given by the specific heat ratio (γ), which is defined as the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv). For an ideal gas, γ is typically greater than 1, indicating that adiabatic processes involve greater changes in pressure and volume compared to isothermal processes. This relationship highlights how the temperature changes under adiabatic conditions differ from those under isothermal conditions.


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