A heat engine uses 100. mg of helium gas and follows the cycle shown in the figure.a) Dete...

Convert the units of mass m of helium from mg to grams as follows:

Substitute for M, and 0.1g for m in the above equation to obtain the number of moles n of helium.

(a)

Use figure, pressure , volume , and temperature at point 1 are given as follows:

Convert the units of from atm to pascal as follows:

The volume at point 1 is given as follows:

Convert the units of from cubic centimetre to cubic metre as follows:

Use ideal gas law obtain the following relation:

Here, is temperature at point1.

Substitute 100kPa for , for , 0.025mol for n, and in the above equation to obtain the value of .

(b)

Use figure, pressure , volume , and temperature at point 2 are given as follows:

Convert the units of from atm to pascal as follows:

The volume at point 2 is given as follows:

Convert the units of from cubic centimetre to cubic metre as follows:

Here, is temperature at point1.

Substitute 500kPa for, for , 0.025mol for n, and in the above equation to obtain the value of .

Use figure, pressure , volume , and temperature at point 3 are given as follows:

Convert the units of from atm to pascal as follows:

Since in isothermal process temperature remains constant, the temperature at point 2 must be equal to temperature at point 3.

Use ideal gas law, for constant temperature the relation between pressure p and volume V is given as follows:

Rearrange the above equation for as follows:

Substitute 500kPa for , 100kPa for , and for in the above equation to obtain the value of as follows:

(b)

The efficiency of the engine is given as follows:

Here, W is work done by engine and Q is heat given to the engine.

Obtain the work done W by the engine as follows:

The heat energy given to the system Q is given as follows:

The efficiency of the engine is given as follows:

Thus, the efficiency of the engine is .

The efficiency of the engine is given as follows:

Here, is minimum temperature, and is maximum temperature.

Substitute 600K for , 3000K for , in the above equation to obtain the efficiency of the engine as follows:

Thus, the efficiency of the engine between maximum and minimum temperature is .