The relaxation time `tau` is nearly independent of applied electric field `E` whereas it changes significantly with temperature `T`. First fact is (in part) responsible for Ohm's law whereas the second fact leads to variation of `p` with temperature. Elaborate why?
The relaxation time `tau` is nearly independent of applied electric field `E` whereas it changes significantly with temperature `T`. First fact is (in part) responsible for Ohm's law whereas the second fact leads to variation of `p` with temperature. Elaborate why?
Text Solution
Verified by Experts
The drift velocity of electrons, `v_(d) =(eE)/m tau, or tau = (mv_(d))/(eE) or tau prop v_(d)//E`
Thys relaxation time depends on velocities of electrons and ions and electric field. The applied electric field affects the velocities of electrons at the order of `1mm//s`, which is very very small and can be neglected. this supports Ohm's law. On the other hand, change in temperature `(TK)` affects velocities of electrons and ions at the order of `10^(2)m//s`. which affect `tau` to great extent and hence to p,i.e., resistivity as `p=m/(n e^(2)tau)`
Thys relaxation time depends on velocities of electrons and ions and electric field. The applied electric field affects the velocities of electrons at the order of `1mm//s`, which is very very small and can be neglected. this supports Ohm's law. On the other hand, change in temperature `(TK)` affects velocities of electrons and ions at the order of `10^(2)m//s`. which affect `tau` to great extent and hence to p,i.e., resistivity as `p=m/(n e^(2)tau)`
Topper's Solved these Questions
Similar Questions
Explore conceptually related problems
Dependence of Spontaneity on Temperature: For a process to be spontaneous , at constant temperature and pressure , there must be decrease in free energy of the system in the direction of the process , i.e. DeltaG_(P.T) lt 0. DeltaG_(P.T) =0 implies the equilibrium condition and DeltaG_(P.T) gt 0 corresponds to non- spontaneity. Gibbs- Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as : " "DeltaG_(P.T) = DeltaH-TDeltaS" ""..."(1) The magnitude of DeltaH does not change much with the change in temperature but the entropy factor TDeltaS change appreciably . Thus, spontaneity of a process depends very much on temperature. For endothermic process, both DeltaH and DeltaS are positive . The energy factor, the first factor of equation, opposes the spontaneity whereas entorpy factor favours it. At low temperature the favourable factor TDeltaS will be small and may be less than DeltaH, DeltaG will have positive value indicated the nonspontaneity of the process. On raising temperature , the factor TDeltaS Increases appreciably and when it exceeds DeltaH, DeltaG would become negative and the process would be spontaneous . For an expthermic process, both DeltaH and DeltaS would be negative . In this case the first factor of eq.1 favours the spontaneity whereas the second factor opposes it. At high temperature , when T DeltaS gt DeltaH, DeltaG will have positive value, showing thereby the non-spontaneity fo the process . However , on decreasing temperature , the factor , TDeltaS decreases rapidly and when TDeltaS lt DeltaH, DeltaG becomes negative and the process occurs spontaneously. Thus , an exothermic process may be spontaneous at low temperature and non-spontaneous at high temperature. When CaCO_(3) is heated to a high temperature , it undergoes decomposition into CaO and CO_(2) whereas it is quite stable at room temperature . The most likely explanation of it, is
For a process top be spontaneous, at constant temperature and pressure, there must be decreases in free energy of the system in the direction of the process, i.e. DeltaG_(P.T.)lt0.Delta_(P.T.)=0 implies the equilibrium condition and DeltaG_(P.T.)gt0 corresponding to non-spontaneity. Gibb's Helmholtz equation relates the free energy change to the enthalpy and entropy change of the process as : DeltaG_(P.T.)=DeltaH-TDeltaS ......(i) The magnitude of Delta H does not change much with the change in temperature but the entropy factor TDeltaS changes appreciably. Thus, spontaneity of a process depends very much on temperature. For edothermic proces, both DeltaH "and " DeltaS are positive. The energy factor,the first factor of equation, opposes the spontaneity whereas entropy factor favours it . At low temperature, the favourable factor TDeltaS will be small and may be less than Delta H, DeltaG will have positive value indicating the non-spontaneity of the process. On raising temperature, the factor TDeltaS increases appreciably and when it exceeds DeltaH,DeltaG would become negative and the process would be spontaneous. For an exothermic process, both DeltaH " and " DeltaS would be negative. In this case, the first factor of equation(i) favours the spontaneity whereas the second factor opposes it. At high temperature, when TDeltaSgt DeltaH, DeltaG will have positive value, showing thereby the non-spontaneity of the process. However, on decreasing temperature, the factore TDeltaSlt DeltaH,DeltaG becomes negative and the process occurs spontaneously. Thus, an exothermic process may be spontaneous at low temperature and non-spontaneous at high temperature. When CaCO_(3) is heated to a high temperature, it undergoes decomposition into CaO and CO_(2) whereas it is quite stable at room temperature. The most likely explanation of it, is:
Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value of zero as their temperature is lowered below a critical temperature T_(C) (0) . An interesting property of super conductors is that their critical temperature becomes smaller than T_(C) (0) if they are placed in a magnetic field, i.e., the critical temperature T_(C) (B) is a function of the magnetic field strength B. The dependence of T_(C) (B) on B is shown in the figure. . In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B_1 (solid line) and B_2 (dashed line). If B_2 is larget than B_1 which of the following graphs shows the correct variation of R with T in these fields?
Dependence of Spontaneity on Temperature: For a process to be spontaneous , at constant temperature and pressure , there must be decrease in free energy of the system in the direction of the process , i.e. DeltaG_(P.T) lt 0. DeltaG_(P.T) =0 implies the equilibrium condition and DeltaG_(P.T) gt 0 corresponds to non- spontaneity. Gibbs- Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as : " "DeltaG_(P.T) = DeltaH-TDeltaS" ""..."(1) The magnitude of DeltaH does not change much with the change in temperature but the entropy factor TDeltaS change appreciably . Thus, spontaneity of a process depends very much on temperature. For endothermic process, both DeltaH and DeltaS are positive . The energy factor, the first factor of equation, opposes the spontaneity whereas entorpy factor favours it. At low temperature the favourable factor TDeltaS will be small and may be less than DeltaH, DeltaG will have positive value indicated the nonspontaneity of the process. On raising temperature , the factor TDeltaS Increases appreciably and when it exceeds DeltaH, DeltaG would become negative and the process would be spontaneous . For an expthermic process, both DeltaH and DeltaS would be negative . In this case the first factor of eq.1 favours the spontaneity whereas the second factor opposes it. At high temperature , when T DeltaS gt DeltaH, DeltaG will have positive value, showing thereby the non-spontaneity fo the process . However , on decreasing temperature , the factor , TDeltaS decreases rapidly and when TDeltaS lt DeltaH, DeltaG becomes negative and the process occurs spontaneously. Thus , an exothermic process may be spontaneous at low temperature and non-spontaneous at high temperature. The enthalpy change for a certain rection at 300 K is -15.0 K cal mol^(-1) . The entropy change under these conditions is -7.2 cal K^(-1)mol^(-1) . The free energy change for the reaction and its spontaneous/ non-spontaneous character will be
Dependence of Spontaneity on Temperature: For a process to be spontaneous , at constant temperature and pressure , there must be decrease in free energy of the system in the direction of the process , i.e. DeltaG_(P.T) lt 0. DeltaG_(P.T) =0 implies the equilibrium condition and DeltaG_(P.T) gt 0 corresponds to non- spontaneity. Gibbs- Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as : " "DeltaG_(P.T) = DeltaH-TDeltaS" ""..."(1) The magnitude of DeltaH does not change much with the change in temperature but the entropy factor TDeltaS change appreciably . Thus, spontaneity of a process depends very much on temperature. For endothermic process, both DeltaH and DeltaS are positive . The energy factor, the first factor of equation, opposes the spontaneity whereas entorpy factor favours it. At low temperature the favourable factor TDeltaS will be small and may be less than DeltaH, DeltaG will have positive value indicated the nonspontaneity of the process. On raising temperature , the factor TDeltaS Increases appreciably and when it exceeds DeltaH, DeltaG would become negative and the process would be spontaneous . For an expthermic process, both DeltaH and DeltaS would be negative . In this case the first factor of eq.1 favours the spontaneity whereas the second factor opposes it. At high temperature , when T DeltaS gt DeltaH, DeltaG will have positive value, showing thereby the non-spontaneity fo the process . However , on decreasing temperature , the factor , TDeltaS decreases rapidly and when TDeltaS lt DeltaH, DeltaG becomes negative and the process occurs spontaneously. Thus , an exothermic process may be spontaneous at low temperature and non-spontaneous at high temperature. For the reaction at 298 K ,2A + B rarr C DeltaH =100 kcal and DeltaS=0.050 kcal K^(-1) . If DeltaH and DeltaS are assumed to be constant over the temperature range, above what temperature will the reaction become spontaneous?
Dependence of Spontaneity on Temperature: For a process to be spontaneous , at constant temperature and pressure , there must be decrease in free energy of the system in the direction of the process , i.e. DeltaG_(P.T) lt 0. DeltaG_(P.T) =0 implies the equilibrium condition and DeltaG_(P.T) gt 0 corresponds to non- spontaneity. Gibbs- Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as : " "DeltaG_(P.T) = DeltaH-TDeltaS" ""..."(1) The magnitude of DeltaH does not change much with the change in temperature but the entropy factor TDeltaS change appreciably . Thus, spontaneity of a process depends very much on temperature. For endothermic process, both DeltaH and DeltaS are positive . The energy factor, the first factor of equation, opposes the spontaneity whereas entorpy factor favours it. At low temperature the favourable factor TDeltaS will be small and may be less than DeltaH, DeltaG will have positive value indicated the nonspontaneity of the process. On raising temperature , the factor TDeltaS Increases appreciably and when it exceeds DeltaH, DeltaG would become negative and the process would be spontaneous . For an expthermic process, both DeltaH and DeltaS would be negative . In this case the first factor of eq.1 favours the spontaneity whereas the second factor opposes it. At high temperature , when T DeltaS gt DeltaH, DeltaG will have positive value, showing thereby the non-spontaneity fo the process . However , on decreasing temperature , the factor , TDeltaS decreases rapidly and when TDeltaS lt DeltaH, DeltaG becomes negative and the process occurs spontaneously. Thus , an exothermic process may be spontaneous at low temperature and non-spontaneous at high temperature. A reaction has a value of DeltaH =-40 Kcal at 400 k cal mol^(-1) . The reaction is spontaneous, below this temperature , it is not . The values fo DeltaG and DeltaS at 400 k are respectively