
A Carnot engine, efficiency 40% and temperature of sink 300 K to increase efficiency up to 60% calculate change in temperature of source.
Answer
483.9k+ views
Hint: As we all know that the efficiency of Carnot engine is \[n = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]
Complete step by step solution:
Given: Carnot engine efficiency, \[{n_1} = 40\% \]
Temperature of sink, \[{T_2} = 300K\]
Efficiency increased to \[{n_2} = 60\% \]
To find:
Change in temperature of the source, now \[{T_1} = ?\]
We know efficiency of Carnot engine is
\[n = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]
\[ \Rightarrow \,\,\,\dfrac{{40}}{{100}} = \dfrac{{{T_1} - 300}}{{{T_1}}}\]
\[ = 4{T_1} = 10T - 3000\]
\[ \Rightarrow \,\,\,6{T_1} = 3000\]
\[ \Rightarrow \,\,\,{T_1} = 500K\] is the temperature of the source initially.
Now to increase efficiency to 60%
\[{n_1} = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]
\[\dfrac{{60}}{{100}} = \dfrac{{{T_1} = 300}}{{{T_1}}}\]
\[ \Rightarrow \,\,\,6{T_1} = 10{T_1} - 3000\]
\[ \Rightarrow \,\,\,{T_1} = 750K\] is the new source temperature.
Hence, the change in temperature of the source is 250K.
Note: If we want to find the change in temperature of the source we have to use the same formula and method.
Complete step by step solution:
Given: Carnot engine efficiency, \[{n_1} = 40\% \]
Temperature of sink, \[{T_2} = 300K\]
Efficiency increased to \[{n_2} = 60\% \]
To find:
Change in temperature of the source, now \[{T_1} = ?\]
We know efficiency of Carnot engine is
\[n = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]
\[ \Rightarrow \,\,\,\dfrac{{40}}{{100}} = \dfrac{{{T_1} - 300}}{{{T_1}}}\]
\[ = 4{T_1} = 10T - 3000\]
\[ \Rightarrow \,\,\,6{T_1} = 3000\]
\[ \Rightarrow \,\,\,{T_1} = 500K\] is the temperature of the source initially.
Now to increase efficiency to 60%
\[{n_1} = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]
\[\dfrac{{60}}{{100}} = \dfrac{{{T_1} = 300}}{{{T_1}}}\]
\[ \Rightarrow \,\,\,6{T_1} = 10{T_1} - 3000\]
\[ \Rightarrow \,\,\,{T_1} = 750K\] is the new source temperature.
Hence, the change in temperature of the source is 250K.
Note: If we want to find the change in temperature of the source we have to use the same formula and method.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
10 examples of friction in our daily life

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Define least count of vernier callipers How do you class 11 physics CBSE

The combining capacity of an element is known as i class 11 chemistry CBSE
