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A gas is contained in a metallic cylinde...

A gas is contained in a metallic cylinder fitted with a piston.the piston is suddenly moved in to compress the gas and is maintained at this position. As time passes the pressure of the gas in the cylinder

A

increase

B

decrease

C

remains constant

D

increase or decrease depending on the nature of the gas.

Text Solution

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The correct Answer is:
To solve the problem step by step, we will analyze the situation involving the gas in the metallic cylinder and the effects of compressing the gas with the piston. ### Step-by-Step Solution 1. **Understanding the Initial Condition**: - A gas is contained in a metallic cylinder with a piston. When the piston is suddenly moved in, the gas is compressed to a smaller volume. **Hint**: Consider how compressing a gas affects its volume and pressure. 2. **Effect of Compression on Volume and Pressure**: - When the piston compresses the gas, the volume of the gas decreases. According to Boyle's Law, if the temperature remains constant, the pressure of a gas increases when its volume decreases. **Hint**: Recall Boyle's Law: \( P \propto \frac{1}{V} \) when temperature is constant. 3. **Heat Generation**: - Compressing the gas increases its internal energy, which raises the temperature of the gas. Since the cylinder is metallic, it can conduct heat away from the gas. **Hint**: Think about how energy transfer occurs in a metallic container. 4. **Heat Radiation to Surroundings**: - As time passes, the gas will radiate heat to the surroundings through the metallic walls of the cylinder. This heat loss will cause the temperature of the gas to decrease. **Hint**: Consider how heat transfer affects the temperature of the gas over time. 5. **Constant Volume Condition**: - After the piston is held in place, the volume of the gas remains constant. According to the ideal gas law \( PV = nRT \), if the volume (V) is constant and the temperature (T) decreases, the pressure (P) must also decrease. **Hint**: Use the ideal gas law to relate pressure, volume, and temperature. 6. **Conclusion**: - Therefore, as time passes and the gas cools down while the volume remains constant, the pressure of the gas in the cylinder will decrease. ### Final Answer: The pressure of the gas in the cylinder will **decrease** as time passes.

To solve the problem step by step, we will analyze the situation involving the gas in the metallic cylinder and the effects of compressing the gas with the piston. ### Step-by-Step Solution 1. **Understanding the Initial Condition**: - A gas is contained in a metallic cylinder with a piston. When the piston is suddenly moved in, the gas is compressed to a smaller volume. **Hint**: Consider how compressing a gas affects its volume and pressure. ...
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Knowledge Check

  • A heat insulating cylinder with a movable piston contins 5 moles of hydrogen at standard temperature and prssure if the gas is cmpressed to quarter of its original volume then the pressure of the gas is increased by (gamma=1.4)

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