acape as the gas is compressed and its temperature won\'tr The difrescoe betwen
ID: 1651940 • Letter: A
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acape as the gas is compressed and its temperature won'tr The difrescoe betwen fast compression and slow compression is theredome Chapter 1 Energy in Thermal Physics 24 escape as the ion and slow compression is therefo In this section I'll consider two idealized ways of compressing an ideal isothertnal compression, which is so slow that the temperature of the gas rise at all; and adiabatic compression, which is so fast that no heat escapes the gas during the process. Most real compression processes will be between these extremes, usually closer to the adiabatic approximation. I' with the isothermal case, though, since it's simpler Thus the he because hea Q is positiva Now let of (or into) In practice If you d the gas will The difference important in thermodynamics. 'l1 stan Suppose, then, that you compress an ideal gas isothermally, that is, w changing its temperature. This almost certainly implies that the process is sistatic, so I can use formula 1.29 to calculate the work done, with P det the ideal gas law. On a PV diagram, the formula P- NkT/V, for const a concave-up hyperbola (called an isotherm), as shown in Figure 1.11. The done is minus the area under the graph: ithoy If it's an The curve e sotherm te of the isotlh To find where f is 5 for a dia any infinit Notice that the work done is positive if V compressed. If the gas V, that is, if the gas is being sothermally, the same equation applies but wit y, that is, the work done on the gas is negative. s the gas compr Meanwhil 1.32, app is compressed isothermally, heat must be flowing out, into the ew ronment. To caleulate how much, we can use the first law of thermodynamics ad the fact that for an ideal gas U is proportional to T This diff the comp pressure gas law; Isotherm Figure 1.11. For isothermal compression of an ideal gas, the PV graph is a concave-up by perbola, called an isotherm As always, the work done is m- nus the area under the graph. Figu for temp V Volume Scuba tanks are usually held under water as they are filled, to prevent the air inside from getting too hot.Explanation / Answer
Solution:
The figure shows an isothermal process for an ideal gas being compressed. That is why the initial volume vi > vf , the final volume. When it is compressed, the pressure increases, but volume decreases. So the isotherm's direction points upwards in the direction from Vi to Vf .
For an isothermal process, the temperature remians constant. This is acheived by making the process infinitesimally slow, so that temperature change does not occur in the process.
Since temperature remains constant , the change in Internal energy is zero. From 1st law of thermodynamics,
for an Isothermal process, dU = Q+W =0 => Q = -W
When heat is added to a system , by compressing it , A positive work is said to be done and W>0 . and Q<0 (this happens because it has to compensate the increased heat due to compression by losing it to the surroundings and thus maintain T constant).
During the expansion, Vi< Vf and W <0 which implies Q is positive.
For expansion , dU =0 , W< 0 , Q>0;
Volume increases for ideal gas Expansion . and Volume decreases for ideal gas Compression.
The above figure shows compression since the Vi is at the right end of the curve. and dU=0 , W>0 and Q<0.
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