A power cycle operates with work of the cycle of 800 Btu and

A power cycle operates with work of the cycle of 800 Btu and heat out of 1800 Btu. What is the thermal efficiency of the system? What amount of work is required to run a heat pump in heating mode to provide heat transfer of 40,000 Btu to a home? Assume the coefficient of performance of the heat pump is 2.8. If Dominion Power charges $3/(100,000 Btu * hour) for electricity, what will it cost per day to run the heat pump in problem #7 for 8 hours each day? An average-size man running creates a 60 lbf horizontal force. How many kilocalories will this person burn by running 5 miles in 45 minutes on a flat, straight course? You must show your calculations to receive credit. Air in a piston-cylinder system is heated in a 2-step process. Initial conditions are pressure of 100 kPa and volume of 0.03 m^3. In the first step volume is constant and pressure increases to 150 kPa. In the second step pressure is constant and volume increases to 0.06 m^3. What is the work (in kJ) for each step of the process? An object of mass 1000 kg is thrown straight up with an initial velocity of 20 m/s. What maximum height in m will the object reach?

Solution

5-----

Thermal efficiency of a system = W/Q

= 800 /1800 = 44.44

So thermal efficiency is 44.44 %.

6----

A heat pump is a device which applies external work to extract an amount of heat Q_C from a cold reservoir and delivers heat Q_H to a hot reservoir.

A heat pump is subject to the same limitations from the second law of thermodynamics as any other heat engine and therefore a maximum efficiency can be calculated from the Carnot cycle. Heat Pumps are usually characterized by a coefficient of performance which is the number of units of energy delivered to the hot reservoir per unit work input.

Given Q_H= 40,000 Btu

COP = 2.8

COP = Q_H / W

W= Q_H / COP = 40,000/2.8 = 14,285 Btu

7 ----

Power charge for ,1 hr and 1000,000 Btu = 3 Dolllar

So Power charge for , 8 hr and 1000,000 Btu = 24 Dollar

As in Problem No 6 - amount required to heat pump is 14,285 Btu

So Power charge for the 8 hr , 14, 285 Btu = [24 * 14,285] / [1000,000]

= 0.3485 Dollar

8--------

Force = 60 lbf

5 miles in 45 min

So 1 miles in 9min

So velocity v= 9 miles/min

Total energy expenditure = energy expenditure value of activity x duration of activity in minutes x your body weight in pounds

Total energy expenditure = 0.09*45*60

= 243 kCal