Chapter 11, Problem 6P

(a)

To determine

Find the temperature difference between oven and kitchen in degree Fahrenheit.

Answer to Problem 6P

The temperature difference between oven and kitchen in degree Fahrenheit is $374\text{F}$.

Explanation of Solution

Given data:

The oven temperature, $T_{\text{Oven}}\left(\text{F}\right)=450\text{F}$.

The kitchen temperature, $T_{\text{Kitchen}}\left(\text{F}\right)=76\text{F}$.

Calculation:

The expression to find temperature difference between oven and kitchen is,

$\Delta T\left(\text{F}\right)=T_{\text{Oven}}\left(\text{F}\right)-T_{\text{Kitchen}}\left(\text{F}\right)$ (1)

Here,

$T_{\text{Oven}}\left(\text{F}\right)$ is the temperature of oven in degree Fahrenheit, and

$T_{\text{Kitchen}}\left(\text{F}\right)$ is the temperature of kitchen in degree Fahrenheit.

Substitute $450\text{F}$ for $T_{\text{Oven}}\left(\text{F}\right)$, and $76\text{F}$ for $T_{\text{Kitchen}}\left(\text{F}\right)$ in equation (1) to find $\Delta T\left(\text{F}\right)$,

$\begin{array}{l}\Delta T\left(\text{F}\right)=\left(450\text{F}\right)-\left(76\text{F}\right)\\ \Delta T\left(\text{F}\right)=374\text{F}\end{array}$

Therefore, the temperature difference between oven and kitchen in degree Fahrenheit is $374\text{F}$.

Conclusion:

Hence, the temperature difference between oven and kitchen in degree Fahrenheit is $374\text{F}$.

(b)

To determine

Find the temperature difference between oven and kitchen in degree Rankine.

Answer to Problem 6P

The temperature difference between oven and kitchen in degree Rankine is $374\text{R}$.

Explanation of Solution

Formula used:

The relationship between degree Rankine $\left(\text{R}\right)$ and degree Fahrenheit $\left(\text{F}\right)$ is,

$T\left(\text{R}\right)=T\left(\text{F}\right)+460$ (2)

Here,

$T\left(\text{R}\right)$ is the temperature in degree Rankine, and

$T\left(\text{F}\right)$ is the temperature in degree Fahrenheit.

Calculation:

Substitute $450\text{F}$ for $T\left(\text{F}\right)$ in equation (2) to find oven temperature value in degree Rankine $\left(\text{R}\right)$,

$\begin{array}{l}{T}_{\text{Oven}}\left(\text{R}\right)=450+460\\ T_{\text{Oven}}\left(\text{R}\right)=910\text{R}\end{array}$

Substitute $76\text{F}$ for $T\left(\text{F}\right)$ in equation (2) to find kitchen temperature value in degree Rankine $\left(\text{R}\right)$,

$\begin{array}{l}{T}_{\text{Kitchen}}\left(\text{R}\right)=76+460\\ T_{\text{Kitchen}}\left(\text{R}\right)=536\text{R}\end{array}$

The expression to find temperature difference between oven and kitchen in degree Rankine is,

$\Delta T\left(\text{R}\right)=T_{\text{Oven}}\left(\text{R}\right)-T_{\text{Kitchen}}\left(\text{R}\right)$ (3)

Here,

$T_{\text{Oven}}\left(\text{R}\right)$ is the temperature of oven in degree Rankine, and

$T_{\text{Kitchen}}\left(\text{R}\right)$ is the temperature of kitchen in degree Rankine.

Substitute $910\text{R}$ for $T_{\text{Oven}}\left(\text{R}\right)$, and $536\text{R}$ for $T_{\text{Kitchen}}\left(\text{R}\right)$ in equation (3) to find $\Delta T\left(\text{R}\right)$,

$\begin{array}{l}\Delta T\left(\text{R}\right)=\left(910\text{R}\right)-\left(536\text{R}\right)\\ \Delta T\left(\text{R}\right)=374\text{R}\end{array}$

Conclusion:

Therefore, the temperature difference between oven and kitchen in degree Rankine is $374\text{R}$.

(c)

To determine

Find the temperature difference between oven and kitchen in degree Celsius.

Answer to Problem 6P

The temperature difference between oven and kitchen in degree Celsius is $207.8\text{C}$.

Explanation of Solution

Formula used:

The relationship between degree Celsius $\left(\text{C}\right)$ and degree Fahrenheit $\left(\text{F}\right)$ is,

$T\left(\text{C}\right)=\frac{5}{9}\left(T\left(\text{F}\right)-32\right)$ (4)

Here,

$T\left(\text{C}\right)$ is the temperature in degree Rankine.

Calculation:

Substitute $450\text{F}$ for $T\left(\text{F}\right)$ in equation (4) to find oven temperature value in degree Celsius $\left(\text{C}\right)$,

$\begin{array}{l}{T}_{\text{Oven}}\left(\text{C}\right)=\frac{5}{9}\left(450-32\right)\\ T_{\text{Oven}}\left(\text{C}\right)=232.2\text{C}\end{array}$

Substitute $76\text{F}$ for $T\left(\text{F}\right)$ in equation (4) to find kitchen temperature value in degree Celsius $\left(\text{C}\right)$,

$\begin{array}{l}{T}_{\text{Kitchen}}\left(\text{C}\right)=\frac{5}{9}\left(76-32\right)\\ T_{\text{Kitchen}}\left(\text{C}\right)=24.4\text{C}\end{array}$

The expression to find temperature difference between oven and kitchen in degree Celsius is,

$\Delta T\left(\text{C}\right)=T_{\text{Oven}}\left(\text{C}\right)-T_{\text{Kitchen}}\left(\text{C}\right)$ (5)

Here,

$T_{\text{Oven}}\left(\text{C}\right)$ is the temperature of oven in degree Celsius, and

$T_{\text{Kitchen}}\left(\text{C}\right)$ is the temperature of kitchen in degree Celsius.

Substitute $232.2\text{C}$ for $T_{\text{Oven}}\left(\text{C}\right)$, and $24.4\text{C}$ for $T_{\text{Kitchen}}\left(\text{C}\right)$ in equation (5) to find $\Delta T\left(\text{C}\right)$,

$\begin{array}{l}\Delta T\left(\text{C}\right)=\left(232.2\text{C}\right)-\left(24.4\text{C}\right)\\ \Delta T\left(\text{C}\right)=207.8\text{C}\end{array}$

Therefore, the temperature difference between oven and kitchen in degree Celsius is $207.8\text{C}$.

Conclusion:

Therefore, the temperature difference between oven and kitchen in degree Celsius is $207.8\text{C}$.

(d)

To determine

Find the temperature difference between oven and kitchen in Kelvin.

Answer to Problem 6P

The temperature difference between oven and kitchen in Kelvin is $207.8\text{K}$.

Explanation of Solution

Formula used:

The relationship between degree Celsius $\left(\text{C}\right)$ and Kelvin is,

$T\left(\text{K}\right)=T\left(\text{C}\right)+273$ (6)

Here,

$T\left(\text{K}\right)$ is the temperature in Kelvin.

Calculation:

Substitute $232.2\text{C}$ for $T\left(\text{C}\right)$ in equation (6) to find oven temperature value in Kelvin,

$\begin{array}{l}{T}_{\text{Oven}}\left(\text{K}\right)=232.2+273\\ T_{\text{Oven}}\left(\text{K}\right)=505.2\text{K}\end{array}$

Substitute $24.4\text{C}$ for $T\left(\text{C}\right)$ in equation (6) to find kitchen temperature value in Kelvin,

$\begin{array}{l}{T}_{\text{Kitchen}}\left(\text{K}\right)=24.4+273\\ T_{\text{Kitchen}}\left(\text{K}\right)=297.4\text{K}\end{array}$

The expression to find temperature difference between oven and kitchen in Kelvin is,

$\Delta T\left(\text{K}\right)=T_{\text{Oven}}\left(\text{K}\right)-T_{\text{Kitchen}}\left(\text{K}\right)$ (7)

Here,

$T_{\text{Oven}}\left(\text{K}\right)$ is the temperature of oven in Kelvin,

$T_{\text{Kitchen}}\left(\text{K}\right)$ is the temperature of kitchen in Kelvin.

Substitute $505.2\text{K}$ for $T_{\text{Oven}}\left(\text{K}\right)$, and $297.4\text{K}$ for $T_{\text{Kitchen}}\left(\text{K}\right)$ in equation (7) to find $\Delta T\left(\text{K}\right)$,

$\begin{array}{l}\Delta T\left(\text{K}\right)=\left(505.2\text{K}\right)-\left(297.4\text{K}\right)\\ \Delta T\left(\text{K}\right)=207.8\text{K}\end{array}$

Therefore, the temperature difference between oven and kitchen in Kelvin is $207.8\text{K}$.

Conclusion:

Hence, the temperature difference between oven and kitchen in Kelvin is $207.8\text{K}$.