At a depth of $$40$$ m, the temperature of the lake is $$12$$ °C and an air bubble has a volume of $$1.0$$ $$cm3$$. The air bubble is rising up to reach the surface of the lake, where the temperature is $$35$$ °C. Find the volume of the air bubble when it reaches the surface of the lake

Question

Infinity Learn · Accepted Answer

Using, $$P1=P2+$$ρgh Here, $$P2=1.013$$×$$105atm$$, $$h=40m$$ρ$$=103$$ kgm−$$3$$ (density$$ of $$water) $$g=9.8ms$$−$$1$$∴   $$P1=1.013$$×$$105+103$$×$$9.8$$×$$40=$$ $$493300$$ Pa Now, $$P1V1T1=P2V2T2$$ Here, $$T1=(12+273)=285K$$,$$T2=(35+273)=308KV1=1$$×$$10$$−$$6m3V2$$ is the volume of the air bubble when it reaches the surface∴ $$V2=P1V1T2T1P2=(493300$$×$$1$$×$$10-6)285$$×$$1.013$$×$$105$$ × $$308=5.26$$ × $$10$$−$$6$$ $$m3$$ $$=$$ $$5.3$$ × $$10$$−$$6$$ $$m3$$

At a depth of 40 m, the temperature of the lake is 12 °C and an air bubble has a volume of 1.0 cm³. The air bubble is rising up to reach the surface of the lake, where the temperature is 35 °C. Find the volume of the air bubble when it reaches the surface of the lake

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At a depth of 40 m, the temperature of the lake is 12 °C and an air bubble has a volume of 1.0 cm3. The air bubble is rising up to reach the surface of the lake, where the temperature is 35 °C. Find the volume of the air bubble when it reaches the surface of the lake

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At a depth of 40 m, the temperature of the lake is 12 °C and an air bubble has a volume of 1.0 cm³. The air bubble is rising up to reach the surface of the lake, where the temperature is 35 °C. Find the volume of the air bubble when it reaches the surface of the lake