A frictionless gas-filled cylinder is fitted with a movable piston, as the figur

Question

A frictionless gas-filled cylinder is fitted with a movable piston, as the figure below shows.

The block resting on the top of the piston determines the constant pressure that the gas has. The height h is 0.123 m when the temperature is 273 K and increases as the temperature increases. What is the value of h when the temperature reaches 302 K? (Ignore any effects of atmospheric pressure. Consider the outside of the piston to be in a vacuum.)

A frictionless gas-filled cylinder is fitted with a movable piston, as the figure below shows. The block resting on the top of the piston determines the constant pressure that the gas has. The height h is 0.123 m when the temperature is 273 K and increases as the temperature increases. What is the value of h when the temperature reaches 302 K? (Ignore any effects of atmospheric pressure. Consider the outside of the piston to be in a vacuum.)

Explanation / Answer

assumption to be made in the problem: 1)assume that the gas used in the problem is ideal gas according to the assumption we can take the ideal gas equation to be valid PV=nRT; given in the problem frictionless piston ==>workdone by the piston =0; according to the ideal gas equation we have P=pressure acting on the gas =constant(given in the problem) n=number of moles of gas =constant(no mass is entering or leaving the container) R=universal gas constant=constant so we have V/T =nR/P = constant value; so we can apply V1/T1 =V2/T2; (assume area of cylinder =A) V1=volume of the gas filled cylinder at initial state=(area of cylinder)*(height of cylinder at initial state(given h1=0.123 m))=A*h1=A*0.123 T1=temperature of gas at initial state in kelvin scale=273 K(given) V2=volume of the gas filled cylinder at final state=(area of cylinder)*(height of cylinder at final state(assume h2))=A*h2 T2=temperature of gas at final state in kelvin scale=302 K (given) ==> A*0.123/273 =A*h2/302 ==> h2=0.136 m height of cylinder at final state=0.136 m

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