A diver releases an air bubble of volume 2.0 cm^3 from a depth of 15 m below the surface of a

step 1 have an air bubble of initial volume v1 equals to 2 .0 meter cube and it is released from the de

A diver releases an air bubble of volume 2.0 cm^3 from a...

A diver releases an air bubble of volume $2.0 \mathrm{~cm}^{3}$ from a depth of $15 \mathrm{~m}$ below the surface of a lake, where the temperature is $7.0^{\circ} \mathrm{C}$. What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is $20^{\circ} \mathrm{C} ?$

Key Concepts

Temperature Conversion

Temperature conversion involves converting temperatures from one scale to another, typically Celsius to Kelvin in gas law calculations, as thermodynamic equations require absolute temperatures. The conversion is done by adding 273.15 to the Celsius temperature, ensuring that temperature values are in Kelvin, which is essential for proper application of the gas laws.

Ideal Gas Law

The ideal gas law defines the relationship among pressure, volume, temperature, and the number of moles of a gas, expressed as PV = nRT. This law is a fundamental tool in understanding gas behavior under various conditions and is applied when the gas is assumed to have negligible intermolecular forces and the volume occupied by gas molecules themselves is considered insignificant.

Combined Gas Law

The combined gas law relates the pressure, volume, and temperature of a fixed amount of gas. It is especially useful for problems where a gas undergoes changes in more than one state variable (pressure, volume, or temperature) simultaneously. This law is expressed mathematically as (P?V?)/T? = (P?V?)/T?, assuming the number of gas molecules remains constant.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. In contexts involving fluids like water, the pressure increases with depth according to the equation P = P? + ?gh, where P? is the atmospheric pressure, ? is the fluid density, g is the acceleration due to gravity, and h is the depth. This concept explains the increased pressure experienced at greater depths in a lake or ocean.

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