Question

Six new prototypes for internal-combustion engines are tested in the laboratory. For each engine, the heat energy input and output per cycle, and the designed number of cycles per second are measured. Rank these engines on the basis of the work they perform per cycle. Rank from largest to smallest. To rank items as equivalent, overlap them.

Answer 1

Concepts and reason

The concept used to solve this problem is work done by the heat engine.

First use the expression of the work done by the heat engine. Then compare the work done by all the given heat engine. Finally arrange the work done by heat engine from largest to smallest.

Fundamentals

The expression for the work done by the heat engine can be expressed as follows,

$W = {Q_{in}} - {Q_{out}}$ …… (1)

Here, ${Q_{in}}$ represents the heat energy taken from the source and ${Q_{out}}$ represents the heat energy taken from the system.

Calculate the work done by the heat engine 1.

Substitute $2000{\rm{ J}}$ for ${Q_{in}}$ and $1000{\rm{ J}}$ for ${Q_{out}}$ in the equation (1) $W = {Q_{in}} - {Q_{out}}$ .

$\begin{array}{c}\\{W_1} = 2000{\rm{ J}} - 1000{\rm{ J}}\\\\{\rm{ = 1000 J}}\\\end{array}$
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Calculate the work done by the heat engine 2.

Substitute ${\rm{1500 J}}$ for ${Q_{in}}$ and $500{\rm{ J}}$ for ${Q_{out}}$ in the equation (1) $W = {Q_{in}} - {Q_{out}}$ .

$\begin{array}{c}\\{W_2} = 1500{\rm{ J}} - 500{\rm{ J}}\\\\{\rm{ = 1000 J}}\\\end{array}$

Calculate the work done by the heat engine 3.

Substitute ${\rm{4000 J}}$ for ${Q_{in}}$ and $3000{\rm{ J}}$ for ${Q_{out}}$ in the equation (1) $W = {Q_{in}} - {Q_{out}}$ .

$\begin{array}{c}\\{W_3} = 4000{\rm{ J}} - 3000{\rm{ J}}\\\\{\rm{ = 1000 J}}\\\end{array}$

Calculate the work done by the heat engine 4.

Substitute ${\rm{3000 J}}$ for ${Q_{in}}$ and $1500{\rm{ J}}$ for ${Q_{out}}$ in the equation (1) $W = {Q_{in}} - {Q_{out}}$ .

$\begin{array}{c}\\{W_4} = 3000{\rm{ J}} - 1500{\rm{ J}}\\\\{\rm{ = 1500 J}}\\\end{array}$

Calculate the work done by the heat engine 5.

Substitute ${\rm{1000 J}}$ for ${Q_{in}}$ and $200{\rm{ J}}$ for ${Q_{out}}$ in the equation (1) $W = {Q_{in}} - {Q_{out}}$ .

$\begin{array}{c}\\{W_5} = 1000{\rm{ J}} - 200{\rm{ J}}\\\\{\rm{ = 800 J}}\\\end{array}$

Calculate the work done by the heat engine 6.

Substitute ${\rm{2000 J}}$ for ${Q_{in}}$ and $500{\rm{ J}}$ for ${Q_{out}}$ in the equation (1) $W = {Q_{in}} - {Q_{out}}$ .

$\begin{array}{c}\\{W_6} = 2000{\rm{ J}} - 500{\rm{ J}}\\\\{\rm{ = 1500 J}}\\\end{array}$

Compare the work done by all the heat engines.

${W_4}{\rm{,}}{W_6}{\rm{ > }}{W_1},{W_2},{W_3}{\rm{ > }}{W_5}$

Ans:

The rank of the work done by heat engines from largest to smallest is ${W_4}{\rm{,}}{W_6}{\rm{ > }}{W_1},{W_2},{W_3}{\rm{ > }}{W_5}$ .