In the figure shown, an ideal diatomic gas is kept in a piston-cylinder arrangement. The walls of cylinder are non-conducting and the piston is also non-conducting and free to slide without friction. Initially the piston is in equilibrium with the gas occupying volume at pressure Now heat is slowly supplied to the gas by the heater till its volume doubles. The change in internal energy of the gas is :
Question
In the figure shown, an ideal diatomic gas is kept in a piston-cylinder arrangement. The walls of cylinder are non-conducting and the piston is also non-conducting and free to slide without friction. Initially the piston is in equilibrium with the gas occupying volume at pressure Now heat is slowly supplied to the gas by the heater till its volume doubles. The change in internal energy of the gas is :
Solution
The question seems to be incomplete as it does not provide the figure mentioned, nor does it provide the specific values for the initial volume and pressure of the gas. However, I can provide a general solution to this problem.
The internal energy change of an ideal gas is given by the equation ΔU = nCvΔT, where n is the number of moles, Cv is the specific heat at constant volume, and ΔT is the change in temperature.
In this case, the volume of the gas doubles at constant pressure, which is an isobaric process. The heat supplied, Q, in an isobaric process is given by Q = nCpΔT, where Cp is the specific heat at constant pressure.
For a diatomic gas, Cp - Cv = R, where R is the gas constant. Therefore, Cv = Cp - R.
Substituting Cv into the equation for ΔU, we get ΔU = n(Cp - R)ΔT.
Since Q = nCpΔT, we can substitute Q/nΔT for Cp in the equation for ΔU to get ΔU = Q - nRΔT.
This equation gives the change in internal energy of the gas in terms of the heat supplied, the number of moles, the change in temperature, and the gas constant. To find the specific change in internal energy for this problem, you would need to know the specific values for these variables.
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