Question

In: Physics

(a) What is the maximum temperature of the gas? (b) What would be the efficiency of an ideal engine with reservoirs

(a) What is the maximum temperature of the gas?

(b) What would be the efficiency of an ideal engine with reservoirs at the maximum and minimum temperatures of this engine? Compare this to the actual efficiency, 0.444.

Expert Solution

(a)

Calculate the temperature at point C using gas laws.

VA/TA = VC/TC

TC = VC × TA/VA

Here, VA is the volume of gas at point A, VC is the volume of gas at point C, TA is the temperature of gas at point A, and TC is the temperature of gas at point C.

Substitute 0.5 m3 for VA, 2 m3 for VC, and 470 K for TA.

TC = 2 m3 × 470 K/0.5 m3

= 1880 K

Calculate the temperature at point B using gas laws.

PB/TB = PA/TA

TB = PB × TA/PA

Here, PA is the pressure of gas at point A, PB is the pressure of gas at point B, and TB is the temperature of gas at point B.

Substitute 1 atm. for PA, 5 atn, for PB, and 470 K for TA.

TB = 5 atm. × 470 K/1 atm.

= 2350 K

Hence, the maximum temperature of gas is 2350 K.

(b)

Calculate the ideal efficiency of the engine.

η = 1 – Tmin./Tmax.

Here, Tmin is the minimum temperature, and Tmax is the maximum temperature.

Substitute 470 K for Tmin, and 2350 K for Tmax.

η = 1 – 470 K/2350 K

= 1 – 0.2

= 0.8

= 80%

Hence, the ideal efficiency of the engine is 80%.

On comparing the ideal efficiency with the actual efficiency of the engine, it is clear that the ideal efficiency is greater than the actual efficiency.

(a) Hence, the maximum temperature of gas is 2350 K.

(b) Hence, the ideal efficiency of the engine is 80%.

Junaid answered 1 year ago

An engine that operates by means of an ideal diatomic ideal gas in a piston with...

An engine that operates by means of an ideal diatomic ideal gas in a piston with 2.70 moles of gas. The gas starts at point A with 3x103 Pa of pressure and 2.5x10-2 m3. To get from B from A, it is expanded by an isobaric process to double the initial volume. From B to C it expands adiabatically until it reaches three times the volume in A. From C to D the pressure decreases without changing the volume and...

Determine what is the temperature of the hot combustion gas that is produced in the engine...

Determine what is the temperature of the hot combustion gas that is produced in the engine of a butanol (C4H9OH)-burning bus that uses ambient air for the combustion. Tip: write the balanced stoichiometric equation for the combustion of butanol assuming air is composed of 80% N2 and 20% O2 by volume, and derive the energy balance of the combustion. Atomic weights: C-12, H-1, O-16, N-14. For butanol: cp = 2 kJ/kg/°C; cv = 1.75 kJ/kg/°C; heat released by combustion, or...

Efficiency An ideal diatomic gas is used in a reversible heat cycle. The gas begins in...

Efficiency An ideal diatomic gas is used in a reversible heat cycle. The gas begins in state A with pressure 100 kPa, temperature300 K, and volume 0.50 L. It first undergoes an isochoric heating to state B with temperature 900 K. That is followed by an isothermal expansion to state C. Finally, an isobaric compression that returns the gas to state A. (a)Determine the pressure, volume, and temperature of state B. (b)Determine the pressure, volume, and temperature of state C....

What is the condition for the system that is in contact with temperature and pressure reservoirs?...

What is the condition for the system that is in contact with temperature and pressure reservoirs? Explain. (Thermodynamics)

1a. What happens to the pressure of an ideal gas if you double its temperature in...

1a. What happens to the pressure of an ideal gas if you double its temperature in a closed volume? And what happens to the pressure of an ideal gas if you double its volume at a fixed temperature?Please explain your answer using the combine gas law. 1b. Based upon the standard molar volume, what volume would 0.500 moles of an ideal gas occupy at STP? And based upon the standard molar volume, what volume would be occupied by 1.00 mol...

An ideal diesel engine uses air as the working fluid and operates with a thermal efficiency...

An ideal diesel engine uses air as the working fluid and operates with a thermal efficiency ?th =0.5 with a rate of heat addition Qin=120 kW. The temperature at the beginning and the end of the addition heat (combustion) are respectively: T2=900 K and T3=2100 K. Assume constant specific heats (Cp and Cv). The air properties at a room temperature T1=293.0 K are: Cp=1.005 kJ/kg.K, Cv=0.718KJ/kg.K, the gas constant of air is R=0.287 kJ/kg.K and the ratio of specific heats...

Efficiency of an engine operating condition to Carnot cycle is equal to ? = 0.45. Temperature...

Efficiency of an engine operating condition to Carnot cycle is equal to ? = 0.45. Temperature and specific volume of the gaseous working medium at the beginning of isentropic compression are T1 = 600 K and v1 = 0.5 m3/Kg respectively. Find the gas properties at all other characteristic points of the cycle and the amount of heat released during isothermal compression. Assume that the mass of 1Kg of the gas undergoes the sequence of processes corresponding to Carnot cycle....

A mole of an ideal gas goes through a cycle of a Carnot engine. Draw the...

A mole of an ideal gas goes through a cycle of a Carnot engine. Draw the pressure vs volume and entropy vs temperature planes for this cycle. What do the diagrams look like when the efficiency of the cycle is 50% and 99%. Then Calculate the work done per cycle by the gas and find the efficiency of the cycle.

Consider an engine in which the working substance is 1.23 mol of an ideal gas for...

Consider an engine in which the working substance is 1.23 mol of an ideal gas for which γ = 1.41. The engine runs reversibly in the cycle shown on the PVdiagram (see figure below). The cycle consists of an isobaric (constant pressure) expansion a at a pressure of 15.0 atm, during which the temperature of the gas increases from 300 K to 600 K, followed by an isothermal expansion b until its pressure becomes 3.00 atm. Next is an isobaric...

At the beginning of compression of an ideal Diesel cycle the gas has a temperature and...

At the beginning of compression of an ideal Diesel cycle the gas has a temperature and pressure of 400C and 90 kN/m2, respectively. The volume ratio of compression is 16:1. The maximum temperature of the cycle is 14000C. Determine, for the cycle, the pressure and temperature at each of the cycle process change points, [8] the work done/kg gas, [4] the thermal efficiency, [4] the work ratio, [3] the mean effective pressure,...