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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

(a) increaes

B

(b) decreases

C

(c) remains the same

D

(d) may increase or decrease depending on the nature of the gas

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the situation step by step, considering the behavior of the gas when it is compressed and how its properties change over time. ### Step-by-Step Solution: 1. **Initial Compression**: When the piston is suddenly moved inwards, the volume of the gas in the cylinder decreases. According to Boyle's Law, for a given amount of gas at constant temperature, the pressure of the gas increases as the volume decreases. 2. **Ideal Gas Law**: The relationship between pressure (P), volume (V), and temperature (T) of an ideal gas is given by the ideal gas law: \[ PV = nRT \] where \( n \) is the number of moles of gas and \( R \) is the ideal gas constant. 3. **Constant Volume**: After the piston is held in position, the volume of the gas remains constant. This means that any changes in pressure must be related to changes in temperature. 4. **Heat Radiation**: The metallic cylinder is not insulated, which means it can lose heat to the surroundings. As time passes, the gas will radiate energy, leading to a decrease in its temperature. 5. **Effect on Pressure**: Since the volume is constant and the temperature is decreasing due to heat loss, we can apply the ideal gas law again. With a constant volume, pressure is directly proportional to temperature: \[ P \propto T \quad \text{(at constant V)} \] Therefore, as the temperature decreases, the pressure of the gas must also decrease. 6. **Conclusion**: After analyzing the situation, we conclude that as time passes, the pressure of the gas in the cylinder decreases. ### Final Answer: The pressure of the gas in the cylinder **decreases**.
To solve the problem, we need to analyze the situation step by step, considering the behavior of the gas when it is compressed and how its properties change over time. ### Step-by-Step Solution: 1. **Initial Compression**: When the piston is suddenly moved inwards, the volume of the gas in the cylinder decreases. According to Boyle's Law, for a given amount of gas at constant temperature, the pressure of the gas increases as the volume decreases. 2. **Ideal Gas Law**: The relationship between pressure (P), volume (V), and temperature (T) of an ideal gas is given by the ideal gas law: \[ ...
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