The change in the magnitude of the volume of an ideal gas when a small additional pressure Δ P is applied at constant temperature is the same as the change when the temperature is reduced by a small quantity Δ T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2…

Question

The change in the magnitude of the volume of an ideal gas when a small additional pressure Δ P is applied at constant temperature is the same as the change when the temperature is reduced by a small quantity Δ T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm respectively. If |Δ T|=C|Δ P|, the value of C in K/atm is .

Accepted Answer

150. Isothermal squeeze: PV= constant gives (|Δ V|)/V=(|Δ P|)/P. Isobaric cooling: V/T= constant gives (|Δ V|)/V=(|Δ T|)/T. Setting the two equal, (|Δ T|)/T=(|Δ P|)/P, so |Δ T|=T/P|Δ P|. C=T/P=(300)/2=150 K/atm.

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