## F.Sc ICS Notes: Physics XI: Chapter 11 Heat and Thermodynamics Numerical Problems

__Estimate the average speed of nitrogen molecules in air under standard conditions of pressure and temperature.__

**Numerical Problem 11.1:**__Show that ratio of the root mean square speeds of molecules of two different gases at a certain temperature is equal to the square root of the inverse ratio of their masses.__

**Numerical Problem 11.2:**__A sample of gas is compressed to one half of its initial volume at constant pressure of 1.25 * 10(5) Nm(-2). During the compressions, 100J of work is done on the gas. Determine the volume of the gas.__

**Numerical Problem 11.3:**__A thermodynamic system undergoes a process in which its internal energy decreases by 300J. If at the same time 120J of work is done on the system, find work done on the system, find the heat lost by the system.__

**Numerical Problem 11.4:**__A Carnot engine utilize an ideal gas. The source temperature is 227 degree Celsius and the sink is 127 degree Celsius. Find the efficiency of the engine. Also find the heat input from the source and the heat rejected to the sink when 10000J of work is done.__

**Numerical Problem 11.5:**__A reversible engine works between two temperatures whose difference is 100 degree Celsius. If it absorbs 746J of heat from the source and rejects 546J to the sink, calculate the temperature of the source and the sink.__

**Numerical Problem 11.6:**__A mechanical engineer develops and engine, working between 327 degree Celsius and 27 degree Celsius and claim correctly? Explain.__

**Numerical Problem 11.7:**__A heat engine performs 100J of work and at the same time rejects 400J of heat energy to the cold reservoir. What is the efficiency of the engine?__

**Numerical Problem 11.8:**__A Carnot engine whose low temperature reservoir is at 7 degree Celsius has an efficiency of 50%. It is desired to increase the efficiency to 70%. By how many degrees the temperature of the source be increased?__

**Numerical Problem 11.9:**__A steam engine has a boiler that operates at 450K. The heat changes water into steam, which drives the piston. The exhaust temperature of the outside air is about 300K. What is the maximum efficiency of the steam engine?__

**Numerical Problem 11.10:**__336J of energy is required to melt 1g of ice at 0 degree Celsius. What is the change in entropy of 30g of water at 0 degree Celsius as it is changed to ice at 0 degree Celsius by a refrigerator?__

**Numerical Problem 11.11:**
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