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An ideal gas undergoes expansion according to the process PV0.5 = constant. The temperature of'the gas during expansion process
- a)does not change
- b)increases
- c)decreases
- d)changes depend on the initial condition
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An ideal gas undergoes expansion according to the process PV0.5 = cons...
∴
for expansion process, V2 > V1
as
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An ideal gas undergoes expansion according to the process PV0.5 = cons...
Expansion of an Ideal Gas
Introduction:
In this problem, an ideal gas undergoes expansion according to the process PV^0.5 = constant, where P is the pressure and V is the volume of the gas. We need to determine how the temperature of the gas changes during this expansion process.
Ideal Gas Law:
The ideal gas law states that for an ideal gas, the product of pressure (P) and volume (V) is directly proportional to the absolute temperature (T) of the gas, given by the equation PV = nRT, where n is the number of moles of gas and R is the gas constant.
Process Equation:
In this problem, we have the equation PV^0.5 = constant. Let's rearrange the equation to isolate pressure:
P = constant / V^0.5
Analysis:
To analyze how the temperature changes during this process, we need to consider the relationship between temperature and pressure according to the ideal gas law.
Direct Proportionality:
From the ideal gas law equation PV = nRT, we can observe that temperature (T) is directly proportional to pressure (P). This means that as pressure increases, temperature also increases, and vice versa, as long as the volume and the number of moles of gas remain constant.
Process Equation:
In the given process equation P = constant / V^0.5, the pressure is inversely proportional to the square root of volume. As the volume increases, the pressure decreases, and vice versa.
Temperature Change:
Since pressure and temperature are directly proportional, and pressure decreases during the expansion process, the temperature of the gas will also decrease. Therefore, the correct answer is option 'C' - the temperature of the gas decreases during the expansion process.
Conclusion:
The temperature of the ideal gas decreases during the expansion process according to the equation PV^0.5 = constant. This is because the pressure is inversely proportional to the square root of volume in this process, leading to a decrease in temperature.
Introduction:
In this problem, an ideal gas undergoes expansion according to the process PV^0.5 = constant, where P is the pressure and V is the volume of the gas. We need to determine how the temperature of the gas changes during this expansion process.
Ideal Gas Law:
The ideal gas law states that for an ideal gas, the product of pressure (P) and volume (V) is directly proportional to the absolute temperature (T) of the gas, given by the equation PV = nRT, where n is the number of moles of gas and R is the gas constant.
Process Equation:
In this problem, we have the equation PV^0.5 = constant. Let's rearrange the equation to isolate pressure:
P = constant / V^0.5
Analysis:
To analyze how the temperature changes during this process, we need to consider the relationship between temperature and pressure according to the ideal gas law.
Direct Proportionality:
From the ideal gas law equation PV = nRT, we can observe that temperature (T) is directly proportional to pressure (P). This means that as pressure increases, temperature also increases, and vice versa, as long as the volume and the number of moles of gas remain constant.
Process Equation:
In the given process equation P = constant / V^0.5, the pressure is inversely proportional to the square root of volume. As the volume increases, the pressure decreases, and vice versa.
Temperature Change:
Since pressure and temperature are directly proportional, and pressure decreases during the expansion process, the temperature of the gas will also decrease. Therefore, the correct answer is option 'C' - the temperature of the gas decreases during the expansion process.
Conclusion:
The temperature of the ideal gas decreases during the expansion process according to the equation PV^0.5 = constant. This is because the pressure is inversely proportional to the square root of volume in this process, leading to a decrease in temperature.
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An ideal gas undergoes expansion according to the process PV0.5 = constant. The temperature ofthe gas during expansion processa)does not changeb)increasesc)decreasesd)changes depend on the initial conditionCorrect answer is option 'B'. Can you explain this answer?
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