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The pressure of a gas varies depends only on its volume & temperature. Increasing the volume by 50% increases the pressure by 125% (keeping other factors constant). Decreasing the temperature by 50% increases the pressure by 700% (keeping other factors constant). By what percent does the pressure increase/decrease if the temperature decreases by 50% and then volume increases by 50%? (Assume there is no addition/subtraction involved anywhere in the relationship)
  • a)
    1000%
  • b)
    1300%
  • c)
    1700%
  • d)
    1900%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The pressure of a gas varies depends only on its volume temperature. ...
Solution: Let the original values for pressure, volume and temperature be P, V and T respectively.
Step 1: T decreases by 50% (keeping V constant): Since P increases by 700%, P1 = P + 7P = 8P
Step 2: V increases by 50% (keeping T constant): Since Pincreases by 125%, P= 8P + 8P(1.25) = 18P
An increase from P to 18P implies an increase of [(18 - 1) x 100]% i.e. 1700% Hence, option 3.
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Most Upvoted Answer
The pressure of a gas varies depends only on its volume temperature. ...
Understanding the Problem
In this scenario, we are analyzing how pressure changes based on variations in volume and temperature. We have two primary relationships to consider:
- Volume Increase: A 50% increase in volume results in a 125% increase in pressure.
- Temperature Decrease: A 50% decrease in temperature results in a 700% increase in pressure.
Calculating Effects on Pressure
1. Effect of Temperature Decrease:
- Initial pressure: P
- Decreasing temperature by 50% increases pressure by 700%.
- New pressure (after temperature change):
P + 7P = 8P (Pressure increases to 8 times the original)
2. Effect of Volume Increase:
- We now take this new pressure (8P) and consider a 50% increase in volume.
- A 50% increase in volume results in a 125% increase in pressure.
- Thus, new pressure after volume change:
8P + 1.25(8P) = 8P + 10P = 18P
Final Calculation of Pressure Change
- Original pressure: P
- Final pressure after both changes: 18P
Percentage Increase in Pressure
- Increase in pressure:
Final Pressure - Original Pressure = 18P - P = 17P
- Percentage increase = (Increase / Original Pressure) * 100 = (17P / P) * 100 = 1700%
Conclusion
Thus, the pressure increases by 1700% when the temperature is decreased by 50% and then volume is increased by 50%. Hence, the correct answer is option 'C'.
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The pressure of a gas varies depends only on its volume temperature. Increasing the volume by 50% increases the pressure by 125% (keeping other factors constant). Decreasing the temperature by 50% increases the pressure by 700% (keeping other factors constant). By what percent does the pressure increase/decrease if the temperature decreases by 50% and then volume increases by 50%? (Assume there is no addition/subtraction involved anywhere in the relationship)a)1000%b)1300%c)1700%d)1900%Correct answer is option 'C'. Can you explain this answer?
Question Description
The pressure of a gas varies depends only on its volume temperature. Increasing the volume by 50% increases the pressure by 125% (keeping other factors constant). Decreasing the temperature by 50% increases the pressure by 700% (keeping other factors constant). By what percent does the pressure increase/decrease if the temperature decreases by 50% and then volume increases by 50%? (Assume there is no addition/subtraction involved anywhere in the relationship)a)1000%b)1300%c)1700%d)1900%Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The pressure of a gas varies depends only on its volume temperature. Increasing the volume by 50% increases the pressure by 125% (keeping other factors constant). Decreasing the temperature by 50% increases the pressure by 700% (keeping other factors constant). By what percent does the pressure increase/decrease if the temperature decreases by 50% and then volume increases by 50%? (Assume there is no addition/subtraction involved anywhere in the relationship)a)1000%b)1300%c)1700%d)1900%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pressure of a gas varies depends only on its volume temperature. Increasing the volume by 50% increases the pressure by 125% (keeping other factors constant). Decreasing the temperature by 50% increases the pressure by 700% (keeping other factors constant). By what percent does the pressure increase/decrease if the temperature decreases by 50% and then volume increases by 50%? (Assume there is no addition/subtraction involved anywhere in the relationship)a)1000%b)1300%c)1700%d)1900%Correct answer is option 'C'. Can you explain this answer?.
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