Physics, 04.03.2020 17:04 nicollexo21

When a metal rod is heated, its resistance changes both because of a change in resistivity and because of a change in the length of the rod. If a silver rod has a resistance of 1.70 Ω at 21.0°C, what is its resistance when it is heated to 180.0°C? The temperature coefficient for silver is α = 6.1 ✕ 10−3 °C−1, and its coefficient of linear expansion is 18 ✕ 10−6 °C−1. Assume that the rod expands in all three dimensions.

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Answer from: tylerkitchen44

$3.34\Omega$

Explanation:

The resistance of a metal rod is given by

$R=\frac{\rho L}{A}$

where

$\rho$ is the resistivity

L is the length of the rod

A is the cross-sectional area

The resistivity changes with the temperature as:

$\rho(T)=\rho_0 (1+\alpha (T-T_0))$

where in this case:

$\rho_0$ is the resistivity of silver at $T_0=21.0^{\circ}C$

$\alpha=6.1\cdot 10^{-3} ^{\circ}C^{-1}$ is the temperature coefficient for silver

$T=180.0^{\circ}C$ is the current temperature

Substituting,

$\rho(180^{\circ}C)=\rho_0 (1+6.1\cdot 10^{-3}(180-21))=1.970\rho_0$

The length of the rod changes as

$L(T)=L_0 (1+\alpha_L(T-T_0))$

where:

L_0 is the initial length at $21.0^{\circ}C$

$\alpha_L = 18\cdot 10^{-6} ^{\circ}C^{-1}$ is the coefficient of linear expansion

Substituting,

$L(180^{\circ}C)=L_0(1+18\cdot 10^{-6}(180-21))=1.00286L_0$

The cross-sectional area of the rod changes as

$A(T)=A_0(1+2\alpha_L(T-T_0))$

So, substituting,

$A(180^{\circ}C)=A_0(1+2\cdot 18\cdot 10^{-6}(180-21))=1.00572A_0$

Therefore, if the initial resistance at 21.0°C is

$R_0 = \frac{\rho_0 L_0}{A_0}=1.70\Omega$

Then the resistance at 180.0°C is:

$R(180^{\circ}C)=\frac{\rho(180)L(180)}{A(180)}=\frac{(1.970\rho_0)(1.00285L_0)}{1.00572A_0}=1.9644\frac{\rho_0 L_0}{A_0}=1.9644 R_0=\\=(1.9644)(1.70\Omega)=3.34\Omega$

Answer from: Quest

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006 kilo calorie

then ,802.3 kilo joule will be = 802.3 $\times$ 0.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

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