Pregunta
- The pressure of a gas is inversely
proportional to its volume and directly
proportional to its absolute temperature.
When the pressure is
pa and the
temperature
, the volume is
. Find the volume when the
pressure is
pa and the
temperature
.
proportional to its volume and directly
proportional to its absolute temperature.
When the pressure is
temperature
pressure is
temperature
Ask by Boone Horton. in Ghana
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
When the pressure is
Pa and the temperature is
K, the volume is 600 cm³.
Solución
To solve the problem, we’ll use the relationship between pressure
, volume
, and temperature
given by:
This can be expressed as:
where
is the proportionality constant.
Step 1: Establish the Relationship
Given two states of the gas:
-
Initial State:
- Pressure
Pa - Temperature
K - Volume
cm³
- Pressure
-
Final State:
- Pressure
Pa - Temperature
K - Volume
- Pressure
Using the proportionality:
Rearranging to solve for
:
Step 2: Plug in the Known Values
Step 3: Simplify the Calculation
Final Answer:
When the pressure is
Pa and the temperature is
K, the volume of the gas is 600 cm³.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Bonus Knowledge
To find the new volume, we can use the Ideal Gas Law which states that
. Given that the pressure is inversely proportional to the volume and directly proportional to the temperature, we can set up a relationship based on the initial and final states.
Using the initial conditions:
-
pa -
cm³ (or L) -
K
And the new conditions:
-
pa -
K
According to the proportions:
Plugging in the values we have:
Cross-multiplying gives:
Simplifying this:
From that, we can find
:
So the volume when the pressure is
pa and the temperature is
K is approximately
.

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