(CHP: 11 NUMERICALS FROM PAST PAPERS)

(CHP: 11  NUMERICALS FROM PAST PAPERS)

1. A Carnot engine whose low temperature reservoir is 200K has an efficiency of 50%. It is desired to increase this to 75%. By how many degrees must the temperature of flow temperature reservoir be decreased if the temperature of the higher reservoir remains constant? (2012)

2. A 200gm piece of metal is heated to 150 C and then dropped into an aluminum calorimeter of mass 500gm, containing 500gm of water initially at 25 C. Find the final equilibrium temperature of the system if the specific heat of metal is 128.100 J/kg-K, specific heat of water is 4200 J/kg-K (2011)

3. A heat engine performing 400J of work in each cycle has an efficiency of 25%. How much heat is absorbed and rejected in each cycle.(2010)

4. A scientist stores 22 gm of a gas in a tank at 1200 atmospheres. Calculate the mass of the gas escaped. (2009)

5. In an isobaric process 2000 J of heat energy is supplied to a gas in a cylinder, the piston of area 2x10-2 m2 moves through 40cm under a pressure of 1.01 x105 N/m2. Calculate the increase in internal energy of the system. (2009)

6. A Carnot engine performs 2000 J of work and rejects 4000 J of heat to the sink. If the difference of
temperature b/w the source and the sink is 85 C, find the temperature of the source and the sink. (2008)

7. A steel bar is 10m in length and -2.5 C. What will be the change in its length when it is at 250 C. (α for the steel is 3.3x10-8 K-1).  (2008)

8. Calculate the density of hydrogen gas, considering it to be an ideal gas, when the root mean square velocity of hydrogen gas molecules is 1850 m/sec at 0 degree Celsius and 1 atm pressure. (2007)

9. A heat engine performs work at the rate of 500 kilowatt. The efficiency of the engine is 30%; calculate the loss per hr.(2007)

10. A Celsius thermometer in laboratory reads the surrounding temperature as 30 C, what is the temperature in Fahrenheit and absolute scale. (2006)

11. Find the change in volume of a brass sphere of 0.6 m diameter, when it is heated from 30 C to 100oC (α 19x10-6 K–1) (2006)

12. A 100 gm copper block is heated in boiling water for ten minutes and then it is dropped into 150 gm if water at 30 C in a 200 gm calorimeter. If the temperature of water is raised to 33.6 C, determine the specific heat of the material of calorimeter. (2005).

13. A brass ring of 20 cm diameter is to be mounted on a metal rod of 20.02 cm diameter at 20 C. To what temperature should the ring be heated? (2005)

14. Calculate the density of hydrogen gas, considering it to be an ideal gas, when the root mean square velocity of hydrogen molecules is 1850 ms-1 at 0 C and 1 atm pressure. (2004)

15. The low temperature reservoir of a Carnot engine is at -3 C and has an efficiency of 40%. It is derived to increase the efficiency to 50%. By how many degrees should the temperature of hot reservoir be increased? (2004)

16. 100 joules of heat energy are supplied to the system at constant pressure. The internal energy of the system is increased by 750 joules and the volume by 4.5 cm3; find the work done against the piston and the pressure on the piston (2003 pre-eng)

17. A Carnot engine has low temperature reservoir at 5 C has an efficiency of 40%. It is desired to increase this efficiency to 50% by what degree should the temperature for high temperature reservoir be increased? (2003 pre-eng, 2003 pre-med)

18. An air storage tank whose volume is 110 liters contains 2 kg of air pressure of 15 atmospheres. How much air would have to be forced into the tank to increase the pressure to 18 atm, assuming no change in temperature? (2003 pre-medical)

19. Find the root mean square velocity of a hydrogen molecule at 100 C. Take the mass of the hydrogen molecule 3.32x10-27 kg and k= 1.38x10-23 J/k (2002)

20. When 2000 J of heat is supplied to a gas in a cylinder at constant pressure of 1.01x105 N/m2, the piston of  the area of cross section 2x10-2 m2 moves through 0.5m. Calculate the work done and the increase in internal energy of the system (2002)

21. A heat engine performs 1000 J of work and at the same time rejects 4000 J of heat energy to the cold reservoir. What is the efficiency of the engine? If temperature difference between the sink and the source is 75 C. Find the temperature of its source. (2002 pre-eng)

22. A cylinder of diameter 1.00 cm at 30 C is to be slid into a hole in a steel plate. The hole has a diameter of 0.99970 cm3 at 30 C. To what temperature must be the plate heated? (2002 pre-eng)

23. If one mole of mono atomic gas is heated at constant pressure from -30 C to 20 C, find the change in its initial energy and the work done during the process. (2001)
Cp = 20.5 J/Mole K and Cv = 12.5 J/Mole K.

24. An ideal heat engine operates in Carnot cycle between the temperature 2007 C and 127 C and it absorbs 600 J of heat energy, find (1) Work done per cycle (2) Efficiency of the engine. (2001)

25. Calculate the volume occupied by a gram mole of a gas at 10 C and pressure of one atmosphere.(2000)

26. In isobaric process when 2000J of heat energy is supplied a gas in a cylinder the piston moves through 0.5m under a constant pressure of 1.01x105 N/m2. If the area of the piston is 2x10-2 m2 calculate the work done and increase in the internal energy of the system. (2000)

27. Find the efficiency of a Carnot Engine working between 100 C and 50 C. (1999)

28. Find the root mean square velocity of a hydrogen molecule at 7 C. Take the mass of a hydrogen molecule to be 3.32x10-27 kg and Boltzmann Constant=1.38x10-23 J/k. (1998)

29. 540 calories of heat is required to vaporize 1gm of water 100 C. Determine the entropy change involved in vaporizing 5gm of water. (One calorie=4.2J) (1998)

30. A glass flask is filled to the mark with 60 cm3 of mercury at 20 c. If flask and its contents are heated to 40 c, how much mercury will be above the mark? (β for glass =9x10-60C-1 and β for mercury= 182x10-6 C-1)

31. A Carnot engine whose low temperature reservoir is at 200K has an efficiency of 50%. It’s desired to increase this to 75%. By how many degrees must the temperature be decreased if higher temperature of the reservoir remains constant? (1997)

32. In an isobaric process when 2000J of heat energy is supplied to a gas cylinder the piston moves through 0.1m under a constant pressure of 1.01x105 N/m2. If the area of the piston is 5x10-2 m2. Calculate the work done and the increase in the internal energy of the system. (1996)

33. Find the root mean square speed of nitrogen molecule at 27 C. Given the mass of the nitrogen molecule to be 4.67x10-25 kg and k=1.38x10-23 J/K. (1996)

34. A meter bar is of steel is at 0 C and another at -2.5 C. What will be the difference between their lengths at 30 C? (1995)

35. A heat engine performs work at the rate of 500 KW. The efficiency of the engine is 30%. Calculate the loss of heat per hour. (1995)

36. 1200 J of heat energy are supplied to the system at constant pressure. The internal energy of the system is increase by 750J and the volume by 4.5 cubic meters; find the work done against piston and the pressure on the piston. (1994)

37. Two vessels of different materials are identical in size and in dimension. They are filled with equal quantity of
ice at 0 C. If ice in both vessels melts completely in 15 minutes and 10 minutes, compare the thermal
conductivity of the metals of both vessels. (1993)
38. One gram of a gas occupied a volume of 24.93 m3 at the pressure of 500 N/m2, find the temperature of the
gas in  C. Given R=8.313 J/mol.K (1991)
39. A cylinder contains an ideal gas below a frictionless piston fitted in it. If the gas in the cylinder is supplied 3000J of the heat and the piston rises by 0.35 m while the internal energy of the work done by the piston.(1991)

40. At the certain temperature the average kinetic energy of the hydrogen molecule is 3.1x10-21 J. if the mass of the hydrogen molecule is 3.1x10-27 kg, find (a) The temperature (b) r.m.s velocity of hydrogen molecule.Given Boltzmann constant= 1.38x10-23 J/K). (1990)

41. An iron ball has a diameter of 5cm and it is too large to pass through of a hole of 0.01mm in the brass plate when the ball and the plate are at the temperature of 30 C. At what temperature the same for the ball and plate, will the ball just pass through the hole?
(α = 1.2x 10-5 C-1 and α = 1.9x10-5 C-1). (1990)

42. Two rod of copper and brass having the same length and cross section are joined end to end. The free end of copper rod is kept at 10 C and the free end of Brass rod is kept at 100 C, calculate the temperature of the junction of the two rod at equilibrium. Assume the thermal conductivity of copper to be 3 times that of the Brass. Neglect heat losses. (1988)

43. The efficiency of the heat engine is 50% if the temperature of the cold reservoir is 300 K , find the temperature of the hot reservoir. (1987)

44. 10 kg of water falls through a distance of 854 m and all the energy effective in heating the water. To what temperature will the water be raised if it was initially at 20 C? Sp heat of water= 4200 J/C.Kg) (1986)