Answer
Verified
395.4k+ views
Hint: As we know that while using a refrigerating device, it is necessary to determine how much cooling effect that the device generates as compared to the energy it is absorbing to function from the external source.
Complete step by step answer:
We have given that,
The coefficient of performance (COP) of a refrigerator $COP = 5$.
The temperature inside the freezer is ${T_L} = - 20^\circ {\text{C}}$.
We have to determine where the surrounding temperature since the heat and work applied is not given so we can assume this refrigerator as the Carnot refrigerator.
We know that $COP$ of a Carnot refrigerator is given by,
$COP = \dfrac{{{T_L}}}{{{T_H} - {T_L}}}$…… (I)
Here, ${T_L}$ is the freezer temperature, ${T_H}$ is the surrounding temperature.
We can substitute here the value of lower temperature and $COP$ to find the temperature of the surroundings. Therefore, we can substitute ${T_L} = - 20^\circ {\text{C}}$ and $COP = 5$ to find the temperature of the surroundings.
Here we can change the following temperature into the kelvin scale for proper calculation.
We know the relation between the Kelvin scale and Celsius scale is given by,
$T\left( K \right) = T\left( {^\circ {\text{C}}} \right) + 273$…… (II)
Now we can substitute ${T_L} = - 20^\circ {\text{C}}$ in equation in (II) to find the value in kelvin scale.
${T_{L1}} = \left( { - 20 + 273} \right)\,{\text{K}}$
$ \Rightarrow {T_{L1}} = 253\,{\text{K}}$
Now we can substitute ${T_{L1}} = 253\,{\text{K}}$ for ${T_L}$ in equation (I) to find the value of higher body temperature.
$
5 = \dfrac{{253}}{{{T_H} - 253}} \\
\Rightarrow 5{T_H} - 1265 = 253 \\
\Rightarrow 5{T_H} = 1518 \\
\Rightarrow {T_H} = 303.6\,{\text{K}} \\
$
Now we can convert the kelvin scale to the Celsius scale using equation (II). So we can substitute ${T_H} = 303.6\,{\text{K}}$ in equation (II) to find the value of ${T_H}$ in Celsius scale.
$
{T_H}^\iota = \left( {303.6 - 273} \right)^\circ {\text{C}} \\
{T_H}^\iota = 30.6^\circ {\text{C}} \\
$
$\therefore$ So we can say that the temperature of the surroundings to which the refrigerator rejects heat is $30.6^\circ {\text{C}}$.
Note:
We can say that here the above problem can be also seen with the help of the absolute thermodynamic scale concept for finding the heat rejected to the warmer surface or heat extracted from the colder surface. We can say that by absolute thermodynamic temperature scale concept,
$\dfrac{{{Q_H}}}{{{Q_L}}} = \dfrac{{{T_H}}}{{{T_L}}}$.
Here, ${Q_H}$ is the heat rejected to the surroundings, and ${Q_L}$ is the heat extracted from the cold surface. ${T_L}$ is the temperature of the cold region in kelvin, and ${T_H}$ is the temperature of the hot region in kelvin.
Complete step by step answer:
We have given that,
The coefficient of performance (COP) of a refrigerator $COP = 5$.
The temperature inside the freezer is ${T_L} = - 20^\circ {\text{C}}$.
We have to determine where the surrounding temperature since the heat and work applied is not given so we can assume this refrigerator as the Carnot refrigerator.
We know that $COP$ of a Carnot refrigerator is given by,
$COP = \dfrac{{{T_L}}}{{{T_H} - {T_L}}}$…… (I)
Here, ${T_L}$ is the freezer temperature, ${T_H}$ is the surrounding temperature.
We can substitute here the value of lower temperature and $COP$ to find the temperature of the surroundings. Therefore, we can substitute ${T_L} = - 20^\circ {\text{C}}$ and $COP = 5$ to find the temperature of the surroundings.
Here we can change the following temperature into the kelvin scale for proper calculation.
We know the relation between the Kelvin scale and Celsius scale is given by,
$T\left( K \right) = T\left( {^\circ {\text{C}}} \right) + 273$…… (II)
Now we can substitute ${T_L} = - 20^\circ {\text{C}}$ in equation in (II) to find the value in kelvin scale.
${T_{L1}} = \left( { - 20 + 273} \right)\,{\text{K}}$
$ \Rightarrow {T_{L1}} = 253\,{\text{K}}$
Now we can substitute ${T_{L1}} = 253\,{\text{K}}$ for ${T_L}$ in equation (I) to find the value of higher body temperature.
$
5 = \dfrac{{253}}{{{T_H} - 253}} \\
\Rightarrow 5{T_H} - 1265 = 253 \\
\Rightarrow 5{T_H} = 1518 \\
\Rightarrow {T_H} = 303.6\,{\text{K}} \\
$
Now we can convert the kelvin scale to the Celsius scale using equation (II). So we can substitute ${T_H} = 303.6\,{\text{K}}$ in equation (II) to find the value of ${T_H}$ in Celsius scale.
$
{T_H}^\iota = \left( {303.6 - 273} \right)^\circ {\text{C}} \\
{T_H}^\iota = 30.6^\circ {\text{C}} \\
$
$\therefore$ So we can say that the temperature of the surroundings to which the refrigerator rejects heat is $30.6^\circ {\text{C}}$.
Note:
We can say that here the above problem can be also seen with the help of the absolute thermodynamic scale concept for finding the heat rejected to the warmer surface or heat extracted from the colder surface. We can say that by absolute thermodynamic temperature scale concept,
$\dfrac{{{Q_H}}}{{{Q_L}}} = \dfrac{{{T_H}}}{{{T_L}}}$.
Here, ${Q_H}$ is the heat rejected to the surroundings, and ${Q_L}$ is the heat extracted from the cold surface. ${T_L}$ is the temperature of the cold region in kelvin, and ${T_H}$ is the temperature of the hot region in kelvin.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE