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17 Nov 2019
An extended rubber band has length 1 when subjected to a stretching force F. Neglecting the volume change on extension, show that (F When a rubber band is stretched adiabatically it becomes warmer. (partialdifferential u/partial differential t)_T = F - T (partialdifferential F/partial differential T)_t When a rubber band is stretched adiabatically it becomes warmer.(You may test this by holding a large rubber band against your lips and quickly stretching it.) Show that for the small temperature rise delta T, which takes place in a reversible adiabatic stretching the temperature change is given by delta T/T = = integral^l_l_0 1/c_1 (partialdifferential F/partial differential T)_t dl Where 1_1 and 1_2 are the initial and final lengths respectively and C_l is the heat capacity at constant length. At moderate extensions it is found that the force at constant length is approximately proportional to the temperature. Show that (partialdifferential u/partial differential t)_T = 0 Point out in detail the analogy to a perfect gas. Consider how the variables of this problem are related to those we use to describe gases. Speculate on the cause of the temperature change
An extended rubber band has length 1 when subjected to a stretching force F. Neglecting the volume change on extension, show that (F When a rubber band is stretched adiabatically it becomes warmer. (partialdifferential u/partial differential t)_T = F - T (partialdifferential F/partial differential T)_t When a rubber band is stretched adiabatically it becomes warmer.(You may test this by holding a large rubber band against your lips and quickly stretching it.) Show that for the small temperature rise delta T, which takes place in a reversible adiabatic stretching the temperature change is given by delta T/T = = integral^l_l_0 1/c_1 (partialdifferential F/partial differential T)_t dl Where 1_1 and 1_2 are the initial and final lengths respectively and C_l is the heat capacity at constant length. At moderate extensions it is found that the force at constant length is approximately proportional to the temperature. Show that (partialdifferential u/partial differential t)_T = 0 Point out in detail the analogy to a perfect gas. Consider how the variables of this problem are related to those we use to describe gases. Speculate on the cause of the temperature change
Collen VonLv2
21 Jul 2019