A sample of an ideal gas is taken through the cyclic process abca as shown in figure. The scale of the vertical axis is set by and . At point a, .
aHow many moles of gas are in the sample?
b.The temperature of gas at point b
c.Temperature of gas at point c
d.The net energy added to the gas as heat during the cycle?
Find the number of moles and the temperature of the gas at points b and c present in the sample using the gas law. Net energy added can be found from the net work done by the gas using the given graph.
Formula is as follow:
Here, p is pressure, v is volume, T is temperature, R is universal gas constant and n is number of moles.
According to the gas law,
From the given graph, at point a,
Hence, the number of moles of gas present in the sample are .
By gas law,
Hence, the temperature of the gas at point b is .
Hence, the temperature of the gas at point c is .
First law of thermodynamics gives,
For isothermal process,
Substitute the values as:
Hence, the net energy added to the gas as heat during the cycle is
Therefore, the number of moles of gas present in the sample,temperature at a point, and heat added can be foundusing gas law.
A gas is to be expanded from initial state i to final state f along either path 1 or path 2 on a PV diagram. Path 1 consists of three steps: an isothermal expansion (work is in magnitude), an adiabatic expansion (work is in magnitude), and another isothermal expansion (work is in magnitude). Path 2 consists of two steps: a pressure reduction at constant volume and an expansion at constant pressure. What is the change in the internal energy of the gas along path 2?
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