The differential relationship has been .
The gas has been termed to be the ideal gas. For an ideal gas at a constant temperature, the relationship of the change in pressure and volume can be given as constant. The relationship has been given with the application of Boyle's law.
The product of the pressure and volume has been a constant quantity for a reaction.
Pressure Volume = Constant
PV = C
V =
Differentiating the equation:
The differential relationship has been .
For more information about pressure at a constant temperature, refer to the link:
Answer:
A differential equation that could describe the relationship of the rate of change of the volume of gas with respect to the pressure is;
V' = .
Explanation:
Boyle's law states that at constant temperature, the pressure of a given mass of gas is inversely proportional to its volume.
That is;
P₁×V₁ = P₂×V₂ or
P×V = Constant, C
That is V =
Therefore, the rate of change of volume of a gas is given as
which gives
That is the rate of change of the volume of gas with respect to the pressure is proportional to the reciprocal of the square of the pressure.
.
V' = .
(2) increases
(3) remains the same
Answer: option (1) decreases.
Explanation:
May be you have experienced that: when you go to the beach, where the atmposhpere pressure is greater than the atmosphere pressure in places that are at higher altitudes, the water takes longer to boil. That is because the boiling temperature is greater, and you need more total heat (more time) to permit the liquid to reach that temperature.
The reason why that happens is because substances boil when the vapor pressure (the pressure of the particles of vapor over the liquid) equals the atmosphere pressure. So, when the atmposhere pressure increases, the temperature at which the vapor pressure reaches the atmosphere pressure also increases, and when the atmosphere pressure decreases, the temperature at which the vapor pressure reaches the atmosphere pressure decreases.
The total amount of energy in the cooler remains the same. The warm soda transfers its heat energy to the ice, causing the soda to cool and the ice to melt. The cooler, soda, and water from the melted ice eventually reach a thermal equilibrium where they have the same temperature.
In the scenario where a student puts a warm can of soda in a cooler filled with ice, the amount of thermal energy in the cooler's system changes due to the process of heat transfer. This process follows the second law of thermodynamics which stipulates that heat tends to flow from hotter objects to colder objects until they reach equilibrium.
In this case, the warmer soda will transfer its heat to the colder ice. During this process, the ice will absorb the heat without a rise in temperature until all of it has melted. This is because this absorbed energy is used to break the bonds holding the ice molecules together in a solid state, causing a phase change to liquid water.
Simultaneously, the soda can's temperature drops as it loses heat to the ice. Eventually, everything in the cooler—the soda, the melted ice water, and the air within—will reach the same temperature, marking the achievement of thermal equilibrium. Therefore, the total amount of energy in the cooler remains the same, it's just transferred (not lost or gained). The energy initially within the can of soda is transferred to the ice, and the overall rise in the cooler’s temperature represent this energy transfer.
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