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A gas has a well-defined mean energy E when its volume is V and mean pressure is p. If the volume of the gas is changed quasi-statically, the mean pres- sure p (and energy E) of the gas will then change accordingly. Suppose that the gas is taken very slowly from a to b (see Fig. 5.18) while the gas is kept thermally insulated. In this case p is found to depend on the volume V in accordance with the relation

A gas has a well-defined mean energy E when its volume is V and mean pressure is p. If the volume of the gas is changed quasi-statically, the mean pres- sure p (and energy E) of the gas will then change accordingly. Suppose that the gas is taken very slowly from a to b (see Fig. 5.18) while the gas is kept thermally insulated. In this case p is found to depend on the volume V in accordance with the relation

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College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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Kindly solve 5.4 question urgent need help me thanks

4.5 Proposed method for producing polarized proton targets In research in nuclear physics and elementary particles, it is, of great interest to do scattering experiments on targets consisting of protons whose spins are preferentially polarized in a given direction. Each proton has a spin and a magnetic moment po=1.4 x 10-23 erg/gauss. Suppose that one tries to apply the method of the preceding problem by taking a sample of paraffin (which contains many protons), applying a magnetic field of 50,000 gauss, and cooling the sample to some very low absolute temperature T. How low would this tem- perature have to be so that, after equilibrium has been reached, the number of proton moments pointing parallel to the field is at least 3 times as large as the number of proton moments pointing in the opposite direction? Express your answer again in terms of the ratio T/TR where TR is room temperature. 5.4 Work done in an adiabatic process A gas has a well-defined mean energy E when its volume is V and mean pressure is p. If the volume of the gas is changed quasi-statically, the mean pres- sure p (and energy E) of the gas will then change accordingly. Suppose that the gas is taken very slowly from a to b (see Fig. 5.18) while the gas is kept thermally insulated. In this case p is found to depend on the volume V in accordance with the relation 7 x V-5/3. What is the work done on the gas in this process? 5.5 Work done in alternative processes connecting the same macrostates The gas of Prob. 5.4 can also be brought quasi-statically from a to b in various other ways. In particular, consider the following processes and calculate for each the total work W done on the system and the total heat Q absorbed by the system when it is brought quasi-statically from a to b. (See Fig. 5.18.) Process a→→b. The system is compressed from its original to its final volume, heat being removed to maintain the pressure constant. The volume is then kept constant and heat is added to increase the mean pressure to 32 × 100 dynes cm 2, Process adb. The two steps of the preceding process are performed in the opposite order. Process ab. The volume is decreased and heat is supplied so that the mean pressure varies linearly with the volume. (10° dynes cm²) 32 PV-5/3 8 V (10³ cm³) Fig. 5.18 Various processes illustrated on a diagram of mean pressure p versus volume V.
Transcribed Image Text:4.5 Proposed method for producing polarized proton targets In research in nuclear physics and elementary particles, it is, of great interest to do scattering experiments on targets consisting of protons whose spins are preferentially polarized in a given direction. Each proton has a spin and a magnetic moment po=1.4 x 10-23 erg/gauss. Suppose that one tries to apply the method of the preceding problem by taking a sample of paraffin (which contains many protons), applying a magnetic field of 50,000 gauss, and cooling the sample to some very low absolute temperature T. How low would this tem- perature have to be so that, after equilibrium has been reached, the number of proton moments pointing parallel to the field is at least 3 times as large as the number of proton moments pointing in the opposite direction? Express your answer again in terms of the ratio T/TR where TR is room temperature. 5.4 Work done in an adiabatic process A gas has a well-defined mean energy E when its volume is V and mean pressure is p. If the volume of the gas is changed quasi-statically, the mean pres- sure p (and energy E) of the gas will then change accordingly. Suppose that the gas is taken very slowly from a to b (see Fig. 5.18) while the gas is kept thermally insulated. In this case p is found to depend on the volume V in accordance with the relation 7 x V-5/3. What is the work done on the gas in this process? 5.5 Work done in alternative processes connecting the same macrostates The gas of Prob. 5.4 can also be brought quasi-statically from a to b in various other ways. In particular, consider the following processes and calculate for each the total work W done on the system and the total heat Q absorbed by the system when it is brought quasi-statically from a to b. (See Fig. 5.18.) Process a→→b. The system is compressed from its original to its final volume, heat being removed to maintain the pressure constant. The volume is then kept constant and heat is added to increase the mean pressure to 32 × 100 dynes cm 2, Process adb. The two steps of the preceding process are performed in the opposite order. Process ab. The volume is decreased and heat is supplied so that the mean pressure varies linearly with the volume. (10° dynes cm²) 32 PV-5/3 8 V (10³ cm³) Fig. 5.18 Various processes illustrated on a diagram of mean pressure p versus volume V.
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