Question

As a budding mechanical engineer, you are called upon to design a Carnot engine that has 2.00 mol of a monatomic ideal gas as its working substance and operates from a hightemperature reservoir at 500°C. The engine is to lift a 15.0-kg weight 2.00 m per cycle, using 500 J of heat input. The gas in the engine chamber can have a minimum volume of 5.00 L during the cycle. (a) Draw a pV-diagram for this cycle. Show in your diagram where heat enters and leaves the gas. (b) What must be the temperature of the cold reservoir? (c) What is the thermal efficiency of the engine? (d) How much heat energy does this engine waste per cycle? (e) What is the maximum pressure that the gas chamber will have to withstand?

Short answer

The pressure volume diagram for the Carnot engine is shown in figure 1.

Step-by-step solution

Identification of given data

The number of moles of monoatomic gas is\(n = 2\;{\rm{mol}}\)

The temperature of high temperature reservoir is\({T_h} = 500\;^\circ {\rm{C}}\)

The mass of weight is\(m = 15\;{\rm{kg}}\)

The height raised by weight is\(h = 2\;{\rm{m}}\)

The het input for engine is\({Q_{labs}} = 500\;{\rm{J}}\)

The minimum volume of the chamber is \({V_1} = 5\;{\rm{L}}\).

Conceptual Explanation

The pressure Vs volume diagram is drawn by taking pressure on vertical axis and volume on the horizontal axis.

Determination of P-V diagram

The pressure volume diagram for Carnot engine is given below:

Figure (1)

The heat enters for the gas in process ab and heat leaving the gas in process cd.

Therefore, the pressure volume diagram for the Carnot engine is shown in figure 1.