If we did all things we are capable of, we would literally astound ourselves.

– Thomas A. Edison

Wednesday, February 21, 2007

Questions from Thermodynamics

(1) In the cyclic process shown in the PV diagram for an ideal gas, the net work done by the gas during one cycle is
(a) 24P0 V0 (b) –24P0V0 (c) – 6πP0V0 (d) 6πP0V0 (e) 4πP0V0
The area enclosed by the closed curve gives the work done. Since the cycle of operations is clockwise (in the PV diagram with P on the Y-axis), the net work done by the gas is positive
Therefore net work done by the system during one cycle = Area of circle.
Since the quantities on the two axes are different, the shape is not rally a circle. The scales of the quantities could have been changed to make it an ellipse. So, treat it as an ellipse and calculate the area as πab where ‘a’ and ‘b’ are the semi-major and semi-minor axes respectively.
So, work done = π[(5P0 –2P0)/2] [(10V0 –2V0)/2] = 6πP0V0
[Note that if the arrow in the diagram shows the processes in the anticlockwise direction, the net work done by the system will be negative].
(2) A refrigerator removes 1000 calories of heat from the ice trays. The coefficient of performance of the refrigerator is 10. Then the work done by the compressor motor is at least
(a) 240 J (b) 420 J (c) 4200 J (d) 42000 J (e) 0.042 J
Coefficient of performance, β = Q2/w where Q2 is the quantity of heat removed from the cold body (inside the refrigerator) and ‘w’ is the work needed to transfer this heat to the hot body (outside).
Therefore w = Q/β = 1000/10 = 100 calories = 420 J, approximately. This is the minimum work to be done by the compressor motor.
(3) An engine takes in 10000 J of heat and rejects 8000 J while operating between temperatures of 900 K and 600 K. The actual efficiency is
(a) 1/5 (b) 2/5 (c) 1/3 (d) 2/3 (e)4/5
This simple question appeared in the Kerala Engineering Entrance 2000 test paper. The actual efficiency is given by η = (Q1 –Q2)/Q1. Note that this will be less than (T1–T2)/T1 in practical heat engines. The efficiency given by the two expressions will be equal in the case of the ideal, perfectly reversible Carnot engine only.
Actual efficiency = (10000–8000)/10000 = 1/5.

Sunday, February 11, 2007

Two Questions (MCQ) on Telescopes

nvppfThe following question appeared in MPPMT 2000 question paper:
The diameter of the objective of a telescope is ‘a’, its magnifying power is ‘m’ and the wave length of light is λ. The resolving power of the telescope is
(a) a/1.22 λ (b) λm/1.22a (c) 1.22a/ λ (d) a/1.22 λm
The magnifying power given in the problem is just a distraction. The limit of resolution of a telescope, which is the minimum angular separation between two objects that can be resolved is given by dθ = 1.22λ/a. The resolving power is the reciprocal of the limit of resolution and is equal to a/1.22 λ. [Option (a)].
Objectives and eye pieces of telescopes are made of achromatic combination of lenses to make them devoid of the defect of chromatic aberration. Consider the following MCQ:
A telescope objective is an achromatic doublet made of crown glass and flint glass lenses. The proper choice for the achromatic combination is
(a) divergent lens of flint glass and convergent lens of crown glass
(b) convergent lens of flint glass and divergent lens of crown glass
(c) both convergent (d) both divergent
(e) as given in options (a) or (b) or (c)
You might be remembering the condition for an achromatic doublet: ω1 /f1+ ω2/f2 = 0, from which ω1/f1= – ω2/f2.
Since the dispersive power ‘ω’ is a positive quantity, the negative sign shows that one lens must be diverging (negative focal length) and the other converging. In a telescope, the objective has to be converging. Therefore, the converging lens should have smaller focal length (larger power) so that when combined with the diverging lens, the combination will still be converging. Crown glass has smaller dispersive power and hence the converging lens should be made of crown glass to satisfy the above condition of achromatism [Option (a)].

Tuesday, February 06, 2007

Kerala Government Medical and Engineering Entrance Examinations-2007

The Commissioner of Entrance Examinations (Govt. of Kerala) has invited applications for the Entrance Examinations for admission to the following Professional Degree courses in Kerala for 2007-08:
(a) Medical (i) MBBS (ii) BDS (iii) BPharm (iv) BSc (Nursing) (v) BSc (MLT) (vi) BAMS (vii) BHMS (viii) BSMS (Siddha) (ix) BSc–Nursing (Ayurveda) and (x) BPharm (Ayurveda) .
(b) Agriculture (i) BSc (Agriculture) (ii) BFSc (Fisheries) (iii) BSc (Forestry)
(c) Veterinary BVSc & AH
(d) Engineering B.Tech [including BTech (Agricultural Engg. / BTech (Dairy Sc. & Tech) courses under the Kerala Agr iculture University]
(e) Architecture B.Arch
Time Table for the Examinations:
The Entrance Examinations will be held in all the District Centres in Kerala, New Delhi and Dubai (UAE), on the dates mentioned below as per Indian Standard Time.
Engineering Entrance Examination (For Engineering courses except Architecture):
23-04-2007 Monday 10.00 A.M. to 12.30 PM Paper-I: Physics & Chemistry.
24-04-2007 Tuesday 10.00 A.M. to 12.30 PM Paper-II: Mathematics.
Medical Entrance Examination [For Medical (including B.Pharm), Agriculture and Veterinary Courses]:
25-04-2007 Wednesday 10.00 A.M. to 12.30 PM Paper-I: Chemistry & Physics.
26-04-2007 Thursday 10.00 A.M. to 12.30 PM Paper-II: Biology.
Application Forms:
The application form and Prospectus will be sold from 07-02-2007 to 05-03-2007 through selected Canara Bank branches in Kerala and outside the State.
Cost of Application form: General candidates: Rs. 700/- ; SC/ST candidates : Rs. 350/- ( Candidates opting Dubai centre should enclose a bank draft for Rs 7000/- along with the application)
Last date and time for receipt of filled in Application Forms: The filled in Application Form along with the OMR DATA SHEET and other relevant documents to be submitted with the Application form is to be sent in the printed envelope bearing the address of the Commissioner for Entrance Examinations supplied along with the application form so as to reach him before 5 p.m. on 07.03 200 7, by Hand Delivery / Registered Post/ Speed Post.
Visit the site
www.cee-kerala.org for complete details regarding the eligibility for applying for these examinations, sale centres of application forms, provision for downloading the application form in the case of certain categories etc. Make it a habit to visit the site to be informed of the information updates in this connection.