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

Question

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

Infinity Learn · Accepted Answer

At constant temperature $$PV=nRTP$$Δ$$V+V$$Δ$$P=0$$⇒Δ$$V=-V$$Δ$$PP----(1)$$ At constant pressure $$VT=nRP$$⇒V∝T⇒Δ$$VV=$$ΔTT⇒Δ$$V=V$$·Δ$$TT----(2)From$$ $$equation(1)$$ and $$equation(2)$$∵VΔ$$TT=-V$$ΔPP ⇒ΔTΔ$$P=TP=3002=150$$

Introduction-thermodynamics

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At constant temperature PV=nRTPΔV+VΔP=0⇒ΔV=-VΔPP----(1) At constant pressure VT=nRP⇒V∝T⇒ΔVV=ΔTT⇒ΔV=V·ΔTT----(2)From equation(1) and equation(2)∵VΔTT=-VΔPP ⇒ΔTΔP=TP=3002=150

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