A 3.00-L tank contains air at 3.00 atm and 20.0^∘ C . The tank is sealed and cooled until the pr

step 1 Hi everyone this is the problem based on ideal gas equation which is given by pv is called to an

A 3.00-L tank contains air at 3.00 atm and 20.0^∘ C . The...

A $3.00-\mathrm{L}$ tank contains air at 3.00 $\mathrm{atm}$ and $20.0^{\circ} \mathrm{C} .$ The tank is sealed and cooled until the pressure is 1.00 atm. (a) What is the temperature then in degrees Celsius? Assume the volume of the tank is constant. (b) If the temperature is kept at the value found in part (a) and the gas is compressed, what is the vohme when the pressure again becomes 3.00 $\mathrm{atm} ?$

Key Concepts

Temperature Conversion (Celsius to Kelvin)

Conversion between Celsius and Kelvin is necessary when applying the gas laws, as these laws require the temperature to be expressed in an absolute scale. The conversion formula is Kelvin = Celsius + 273.15, ensuring that temperature values are in the proper units for calculations involving gas behavior.

Ideal Gas Law

The ideal gas law, expressed by the equation PV = nRT, relates the pressure, volume, temperature, and quantity of a gas. It provides the foundation for understanding gas behavior under various conditions and is central to problems where gas properties change, such as cooling at constant volume or compression at constant temperature.

Constant Volume Process (Pressure-Temperature Relationship)

In a process where the volume of the gas is held constant, the pressure of the gas is directly proportional to its absolute temperature (P ? T). This is a consequence of the ideal gas law and is used to determine how changes in temperature affect gas pressure when volume remains fixed.

Isothermal Process (Boyle’s Law)

During an isothermal process, the temperature of the gas remains constant. According to Boyle’s law, under these conditions, the pressure of the gas is inversely proportional to its volume (P ? 1/V). This relationship is essential when analyzing situations where the gas is compressed or expanded while maintaining a constant temperature.

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