Why is the PV curve for an adiabatic process steeper than that for an isothermal process derive expression for work done in adiabatic process?

PV diagram – Work done in the adiabatic process To differentiate between isothermal and adiabatic curves in the PV diagram, the adiabatic curve is drawn along with the isothermal curve for Tf and Ti. Note that the adiabatic curve is steeper than an isothermal curve. This is because γ > 1 always.

Which has greater slope adiabatic or isothermal?

It states that the volume of an ideal gas at constant pressure is directly proportional to the absolute temperature.

Which is steeper out of isothermal and adiabatic curves for the same gas?

The adiabatic curve is steeper than the isothermal curve, in both the processes of expansion and compression. To reach a same height in a longer distance means lower slope of the line. Hence adiabatic curve is more steeper than isothermal curve.

Which process has a larger slope on PV diagram?

STATEMENT-2: In a p-V diagram, the magnitude of the slope is greater for an adiabatic process than for an isothermal process.

Why does the Adiabat of an ideal gas fall faster than its isotherm?

The result is that, for the adiabatic process, the pressure is inversely proportional to the volume raised to a power greater than one – a stronger inverse dependence than for the isothermal case, which implies that pressure falls more rapidly as volume increases.

How does an adiabatic process differ from an isothermal process?

The most significant difference between adiabatic process and isothermal process is that in an adiabatic process there is no change in the heat of the system and there is no heat transfer while in an isothermal process in order to maintain a constant temperature of the system heat is transferred from and to the …

How do you determine which slope is greater?

When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line, . The greater the slope, the steeper the line. The next example shows a line with a negative slope.

How can you tell the difference between adiabatic and isothermal curves?

The curve showing the relation between pressure and volume of a given mass of gas when the flow of heat into or out of the gas is stopped is called its adiabatic curve. If isothermal and adiabatic curves be plotted on the same p–v diagram (Fig. 8.4), then the adiabatic curve would be steeper than the isothermal curve.

Which curve have greater slope in PV diagram isotherm or adiabatic curve?

A and B are the slopes of the isothermal and adiabatic curves respectively. We can see from the graph, that the slope of adiabatic is higher than that of the isothermal process.

What is the slope of isotherm on a PV graph?

Isothermal curve slope =γ× adiabatic curve slope.

When an ideal gas expands adiabatically its temperature?

What happens to the temperature of an ideal gas in an adiabatic expansion? An adiabatic expansion has less work done and no heat flow, thereby a lower internal energy comparing to an isothermal expansion which has both heat flow and work done. Temperature decreases during adiabatic expansion.