Question

A piston cylinder device whose piston is resting on top of a set of stops initially contains 0.5kg of helium gas at 100kPa and 25C. The mass of the piston is such that 500kPa of pressure is require to raise it. How much heat must be transferred to the piston before the piston starts rising? The specific heat of helium at room temperature is Cv=3.1156kJ/kg K.

Answer 1

The question involves using the ideal gas law to calculate the change in temperature needed for a piston to begin rising within a piston-cylinder device containing helium, and subsequently calculating the heat transferred using the specific heat at constant volume.

Step-by-step explanation:

The subject of this question is Physics, specifically related to thermodynamics and the behavior of gases within a piston-cylinder arrangement. To determine how much heat must be transferred to the piston before it starts rising, we need to use the formula Q = mCvΔT, where Q represents the heat transferred, m is the mass of the gas, Cv is the specific heat at constant volume, and ΔT is the change in temperature.

To find ΔT, we use the ideal gas law to calculate the final temperature at which the pressure exerted by the helium gas equals 500 kPa. Assuming ideal gas behavior, we have the initial state (P1, V1, T1) and the final state (P2, V2, T2), with P2 = 500kPa (since the piston requires 500 kPa to raise), V1 = V2 (piston hasn’t moved yet), and T1 = 298K (temperature converted from 25°C to Kelvin).

Using the ideal gas law P1V1/T1 = P2V2/T2 and substituting the known values, we can solve for T2. Once T2 is found, ΔT = T2 - T1. Finally, we use the heat transfer formula to calculate Q. The Cv value for helium provided, 3.1156 kJ/kg°K, will be used alongside the mass of 0.5kg. This will give us the required heat that must be transferred.