Chapter 13, Problem 20P

To determine

(a) To determine:

The values of the temperatures of the interior of the Earth and the Sun in Kelvin

Answer to Problem 20P

Solution:

The temperatures of the interiors of the Earth and the Sun in Kelvin are 4273.15 K and$15\times {10}^{6}K$, respectively

Explanation of Solution

Given:

Temperature of interior of the Earth, $T_E=4000°C$

Temperature of the interior of the Sun, $T_S=15\times {10}^6°C$

Formula used:

$T\left(K\right)=T(°C)+273.15$

Calculation:

The conversion of temperature from Celsius scale to Kelvin is given by,

$T\left(K\right)=T(°C)+273.15$

Therefore, for the interior of the Earth, $T\left(K\right)=4000°C+273.15=4273.15K$

For the interior of the Sun, $T\left(S\right)=15\times {10}^6°C+273.15=15\times {10}^{6}K$

Therefore, for the interior of the Earth, $T\left(K\right)=4000°C+273.15=4273.15K$

For the interior of the Sun, $T\left(S\right)=15\times {10}^6°C+273.15=15\times {10}^{6}K$

To determine

(b) To determine:

The percent error made in each case if a person forgets to change from °C to K

Answer to Problem 20P

Solution:

The percentage errors for the Earth and the Sun are 6.83% and$1.8\times {10}^{-3}\%$, respectively.

Explanation of Solution

Given:

Temperature of interior of the Earth, $T_E=4000°C$

Temperature of the interior of the Sun, $T_S=15\times {10}^6°C$

Formula used:

Calculation:

Percentage error = $\frac{T(K)-T(°C)}{T(°C)}\times 100$

Therefore, percentage error for $T_E\frac{4273.15-4000}{4000}\times 100=6.83\%$

Percentage error for $4273.15Kand15x{10}^{6}K$