Pressure-volume relation of gas
The above diagram shows the pressure-volume relation of
moles of an ideal gas in state
and state
Which of the following statements is true?
The internal energies of
and
are the same.
If we change the state of the gas from
to
as shown in the above diagram, then the temperature of the gas will increase.
The amount of the heat emitted from the state change
is
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Looking at the transition of the state of the ideal gas from A to B in the diagram, we can observe that the factor by which the volume of the gas is decreased is equal to that by which its pressure increased.
The ideal gas equation is PV= nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, R is the molar gas constant and T is its temperature. Since the factor by which V is decreased while transitioning from state A to state B is equal to that by which P increased while transitioning from state A to state B, the product of P and V is constant while transitioning from state A to state B, implying that T must be constant as well while transitioning from state A to state B.
The internal energy of a gas is a function of its temperature. Therefore, since the temperature of the gas is constant while transitioning from state A to state B, the internal energy of the gas in state A is equal to that in state B. No net flow of heat occurs to or from the gas while transitioning from state A to state B.
Thus, the only true statement is a.