A gas has experienced a small increase in volume but has maintained the same pressure and number of moles. According to the ideal gas law, how has the temperature of the gas changed?
A. It has increased two times.
B. It has increased slightly.
C. It has decreased slightly.
D. It has stayed the same.
Answer (2)
The ideal gas law states that P V = n RT .
Since pressure ( P ) and the number of moles ( n ) are constant, volume ( V ) and temperature ( T ) are directly proportional: V = k T .
A small increase in volume therefore implies a slight increase in temperature.
The temperature of the gas has increased slightly. $\boxed{It has increased slightly.}
Explanation
Understanding the Problem We are asked to determine how the temperature of a gas changes when its volume increases slightly, while the pressure and number of moles remain constant, according to the ideal gas law.
Stating the Ideal Gas Law The ideal gas law is given by the equation: P V = n RT where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant,
T is the temperature of the gas.
Simplifying the Equation In this scenario, the pressure P , the number of moles n , and the ideal gas constant R are all constant. Therefore, we can rearrange the ideal gas law to express the relationship between volume and temperature: V = P n R T Since n , R , and P are constant, the term P n R is also constant. Let's call this constant k :
k = P n R So, the equation becomes: V = k T
Determining the Change in Temperature This equation shows that the volume V and the temperature T are directly proportional. If the volume increases, the temperature must also increase to maintain the equality. Since the volume has experienced a small increase, the temperature must have increased slightly.
Conclusion Therefore, according to the ideal gas law, if a gas experiences a small increase in volume while maintaining the same pressure and number of moles, the temperature of the gas has increased slightly.
Examples
The ideal gas law is used in various real-world applications, such as designing engines, predicting weather patterns, and understanding the behavior of gases in industrial processes. For example, when designing an internal combustion engine, engineers use the ideal gas law to calculate how the temperature and pressure of the air-fuel mixture change during the compression and expansion strokes. This helps them optimize the engine's performance and efficiency. Similarly, meteorologists use the ideal gas law to predict how changes in temperature and pressure affect the volume of air masses, which is crucial for forecasting weather patterns. In chemical engineering, the ideal gas law is used to determine the amount of gas produced or consumed in a chemical reaction, which is essential for designing and operating chemical plants.
According to the ideal gas law, when a gas experiences a slight increase in volume while maintaining constant pressure and number of moles, its temperature must have increased slightly. Therefore, the answer is B. It has increased slightly.
;
